<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>2113100 - Disclosure - Commitments and Contingencies</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000910108</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>lxp_CommitmentsAndContingenciesAbstract</ElementName><ElementPrefix>lxp_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Commitments and Contingencies [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_CommitmentsAndContingenciesDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-family:Times New Roman;font-size:10pt;"&gt;&lt;div style="line-height:120%;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;text-decoration:underline;"&gt;Commitments and Contingencies&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;padding-left:48px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;padding-left:48px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In addition to the commitments and contingencies disclosed elsewhere and previously disclosed, the Company has the following commitments and contingencies.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;padding-left:48px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;padding-left:48px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The Company is obligated under certain tenant leases to fund the expansion of the underlying leased properties. The Company, under certain circumstances, may guarantee to tenants the completion of base building improvements and the payment of tenant improvement allowances and lease commissions on behalf of its subsidiaries. As of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company had two outstanding guarantees for (1) the completion of the base building improvements and the payment of a related tenant improvement allowance for an office property in Orlando, Florida, which the unfunded amounts were estimated to be &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$3,694&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and (2) the payment of a tenant improvement allowance of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$596&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for a property in Allen, Texas.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;padding-left:48px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;padding-left:48px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;From time to time, the Company is directly and indirectly involved in legal proceedings arising in the ordinary course of  business. Management believes, based on currently available information, and after consultation with legal counsel, that although the outcomes of those normal course proceedings are uncertain, the results of such proceedings, in the aggregate, will not have a material adverse effect on the Company's business, financial condition and results of operations.&lt;/font&gt;&lt;/div&gt;&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for commitments and contingencies.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.25)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 825

 -SubTopic 20

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6449706&amp;loc=d3e16207-108621



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 460

 -SubTopic 10

 -Section 50

 -Paragraph 8

 -URI http://asc.fasb.org/extlink&amp;oid=6398077&amp;loc=d3e12565-110249



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 450

 -SubTopic 20

 -Section 50

 -Paragraph 4

 -URI http://asc.fasb.org/extlink&amp;oid=25496072&amp;loc=d3e14435-108349



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 440

 -SubTopic 10

 -Section 50

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=6394976&amp;loc=d3e25287-109308



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Commitments and Contingencies</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Commitments and Contingencies</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.lxp.com/role/CommitmentsAndContingencies</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
