You say that he was injured during WW1, and that you have an Ancestry account. Have you looked at the pensions database under military? There's a few Thomas Lynchs... Pension applications tend to include their service records.

There's also 32 men called TL with a silver war badge...

Also, if he was not well enough to serve with his regiment, but reasonably fir, he might have been transferred to the Labour Corps.