Thomas Stratford Lyons or Hynes of Kildare. Ploughman / Convict 1825

I am looking for the family of a Thomas Stratford (Edward Lyons) or Hynes of Kildare who was convicted of Horsetheft and transported to Australia in 1825 aboard the vessel the Lonach. His wife(?) and two children followed him in 1834 on the ship Andromeda II.

Problem. His name... is he Edward Lyons as he goes by in Australia, Thomas Stratford Lyons from a birth cert for his daughter? Or Thomas Stratford Hynes a ploughman from Kildare?

Margaret his daughter has a possible birth cert in 1820 from Baltinglass, Wicklow and Kildare, Ireland to Thos Stratford Lyons and Mary Woods. Are they the same couple? They also had a son Edward in 1825 just as his father was leaving for Australia. I can't find a birth cert for anyone except Margaret. Nor can I find a marriage or birth cert - or any other family for Thomas Stratford Lyons (Hynes)  or Mary Woods (if Woods is her family name).
The Convict records are
https://convictrecords.com.au/convicts/hynes/thomas/136492
The family traveling records Original data:New South Wales Government. Musters and other papers relating to convict ships. Series CGS 1155, Reels 2417-2428. State Records Authority of New South Wales.