I have been thinking about this for the past couple days at work. (I have a very boring job) and I have come up with a couple of ways.
1. Better cooperation with Air Canada, hopefully increasing their loads on the YYZ-WAW route.
2. No benefit in America, all that changes is that alliance with American is dissolved and a new one is formed with United, so really not much difference.
3. More codesharing with Lufthansa on all the Germany-Poland routes which will reduce competition and increase profits.
4. Little more cooperation with SAS and Austrian, that with some codeshares will free up some LOT aircraft to open new routes in Europe.
5. So that is about it for the benefits. They really wont contribute much to Star as they only give star about 10 new cities if that. So basically how else will Star help LOT? I think LOT may need to open some new intercontinental routes like to Miami or somewhere in Asia, because I worry that with their small network, joining Star may be the first step to them being swallowed up by Lufthansa and basically being turned into a regional carrier.