Yes, you can earn UA miles for an OS flight "operated by Tyrolean." I did so earlier this summer, no problem at all, as part of the big UA business class fare sale (the OS segments were in Z).

It's always the operating carrier which matters; however, Tyrolean is Austrian as far as that goes, IIRC. It's like earning miles on a United flight operated by SkyWest, for example.

This means that if the fare class on your LX-operated TG flight is eligible for earning UA credit by LX's rules, you should be OK. Now, finding out what fare class it's in is another matter...