Matthew Lynch returned to England / arrived in London from NY on 27 Mar. 1928.
He gave his occupation as man servant, and his address as Newcastle, Kells. Co Meath.
I dont know if he went back to Ireland or stayed in London.
In April 1937 Matthew made an enquiry about his army discharge papers
Address at that time was - 73 Pembroke Rd., Erith, Kent
(see his WW1 papers)
See the following -
Electoral rolls 1949, 1951, 1952, 1953 Matthew Lynch at Belgrave Mews, Westminster.
Electoral Rolls in 1958, 1959, 1960 at Sussex Street Westminster is Matthew Lynch and William Lynch.
Unfortunately, since you are not providing any detail that you have about Matthew, there is very little we can do to assist.