When booking with Thomson Airways how can I select Lithuania as my country?

There are three addresses the airline might ask for.

When entering passenger mailing address, you generally can enter whatever you want, so in your case just enter some address in Latvia. I have never seen or heard of it to be ever checked. Notably many accepted travel documents - such as passports - do not have your address at all. Many years ago this address was used to send paper tickets to you, but nowadays the main purpose of asking for this seem to be that they could send you spam. The only exception is if you order a tour package from them, as they might need to send you paper vouchers or some other paperwork.

Passenger billing address is used by the credit card processor. Depending on the processor it might or might not matter (for example, in US for most processors only ZIP code matters). The easiest way to check this is to try to book and see if your payment is approved. If it is, you're generally good to go, although you might be asked to see your credit card at check-in.

Finally, passenger destination address in a destination country is asked by some airlines at check-in. This seem to be the requirement of the destination country's government, and passed to them by the airline as-is. Here you need to be careful, as making this one up might possibly lead to much more detailed immigration inspection such as when a friend of mine wrote that address as "under Brooklyn bridge".

PS. Glancing at this Thomson site, it misses quite a few countries.