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Fair Value Measurements - Additional Information (Details) - MutualFund | Sep. 30, 2022 | Dec. 31, 2021
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Fair Value Disclosures [Abstract] |  |
Number of mutual fund investment | 4 | 4

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- Definition Number of mutual fund investment. + References No definition available. + Details
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Namespace Prefix: | lgl_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | instant

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- References No definition available. + Details
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Namespace Prefix: | us-gaap_
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Balance Type: | na
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