Sorry...takes me years to wander back through. I've checked the compiled 19th Century Church registers of Bermuda. Must baptisms, marriages, and burials are listed by political/Church of England parish. No listing for other denominations except Presbyterians and Methodists, for each of which Bermuda-wide listings are shown. Seperate listing also for HM Dockyard. Lots of Dunscombs, but only two Lydias, both Presbyterian (doubtless from Christchurch, on Dunscomb Road, in Warwick).
From Presbyterian Baptisms:
Lydia Lea Dunscomb, born 3 August, 1846, baptised 3 Nov., 1846. Father: Richard Vesey (Dunscumb? Veseys are a notable Bermuda family). Mother: Elizabeth Dunscomb.
Other children of same parents:
Adelaide Vesey Dunscomb, born 01/02/1831; Susan Smith Dunscomb, born 10 June, 1832; Elizabeth Dorcas Dunscomb, born 10 August, 1834; Richard Thomas Dunscomb, born 30 April, 1837.
A Lydia Lee Dunscombe, of Paget, age unknown, is listed under Presbyterian burials, ? January, 1913.
Lydia Jane Dunscomb, born 29 March, 1862. Baptised 13 April, 1862. Father: Edward Dunscomb (Edward B. Dunscomb). Mother: Catherine Dunscomb (Catherine Jane Dunscomb).
Others with same parents: Edward Dunscomb, born ?, baptised 25/07/1858; Frances Catherine Dunscomb, born ?, baptised 27/11/1860; Eliza Susan Dunscomb, born ?, baptised 18/04/1869. Same father?: Edward Arnold Dunscomb, born 13/12/1884, baptised 01/03/1885. Father: Edward B. Dunscomb. Mother: Alice Dunscomb.
Haven't checked for burial or mariages of any parents or siblings yet, but doubtless there is a lot more to be unearthed from the book. Given the first Lydia is possibly the one shown buried in Bermuda, the likely emigrant is the latter (not listed under the Presbyterian burials).