I think you should consider leaving the airport and finding something to do for a while in Windsor or London. It'll probably get a bit tedious spending more than a couple of hours in the lounge unless you have something you can be doing.

If you want to spend some time out of the airport then just follow the signs to arrivals rather than flight connections. As long as Israeli (I'm guessing as you called TLV home) citizens can enter the UK without a visa then this will be OK.

You'll be fine as long as you have your onward boarding pass, you can just turn up at T1 later and go through security. If you don't have your BP then arrive slightly earlier at T1 and go to the BA check-in desks before going through security.

No need to spend all the time in the airport (although might be OK if you like shopping, or have work to do), there's threads on the UK and Ireland forum with ideas for things to do nearby.

If you've not been to T1 before, the lounge is located near to gate 5. It should be well signposted. The lounge is a former bmi lounge so is a totally different style to what BA usually has (Galleries/Terraces). There's only one lounge, there's no 'first' lounge in this terminal for OW Emeralds (BA Gold / AA EXPlat)