Myself, I wouldn't bother with splitting the time between arrivals and departures lounges - just park yourself in one place and relax. Unless, of course, you have a real yen to see every possible lounge.

You might be able to get into the new BA First lounge in T1 if it's not busy and someone is looking kindly on you. (I think it's open already; if it isn't yet it soon will be.) BA F and J lounges are both good places to kill quite a few hours with the papers, magazines and drinks on offer.

You might want to have a look at the T1 departures lounge map when planning what to do. The only "sit down restaurant" in T1 is Est Est Est which is fine although nothing wildly special.

It will take you some time to get across from T3 to T1, whether you do it airside through the Flight Connections Centre or landside after clearing immigration and customs. That'll probably account for the best part of an hour after your technical "arrival" at the gate at T3, where there are some long walks for everyone. You'll probably get called for your LHR-LIN flight about 30 minutes or so before departure, so in reality you've only got something like 3.5 hours to kill. Take a leisurely hour and a half for lunch and a gentle stroll around the shops, and you won't be bored even if you just go to T1 and do nothing else.