Although it is especially difficult to read, Thomas Edward Lodington is mentioned in Thomas Lodington's Will (it was written in 1845, obviously before his son's death the same year).
No mention of the children though.
It does mention all the following, though:
Ann Ramsay (née Lodington), daughter.
Thomas Edward Lodington, son.
Meliora Down (née Lodington), daughter.
Henry Parker Lodington, son
William (Stewart) Lodington, son.
George Jackson, son-in-law.
Camilla Mary Basset Soares (née Lodington), daughter.
Sarah Ellen Bishop (née Lodington), daughter.
Francis William Lodington, nephew (although it actually seems he's a cousin)
Henry John Lodington, nephew (but not by name, only as "my dear nephew, his brother", which refers to Francis William Lodington)
It also mentions portraits of the father of Francis William and Henry John Lodington.
It also mentions a portrait given to Ann Ramsay of her brother Thomas.
If only there was a chance these portraits remained in the family... I can but hope somewhere they do.
By the way, I did not know Ann Lodington had married, so now I have a new lead on the Ramsay family to follow-up.