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Michael Hughes was/is a very common name in Ireland. Hughes and Lynskey are common names in Co. Mayo but not in Co. Leitrim. I searched on the subscription site Roots Ireland and there were no Michael Hughes baptismal records in Mayo in 1836-1837 but there was an 1836 record in Leitrim. See below. I don't believe this is for your Michael. ( We really need his parents names to confirm any record located). I also did not find marriage record for the couple.
Any other rinformation. Children born In Ireland?
Name:Michael HughesDate of Birth:
Date of Baptism:03-Jan-1836Address:BohyParish/District:GORTLETTERAGH ROMAN CATHOLICGender:MaleCountyCo. Leitrim
Father:Terence HughesMother:Bridget Gray