Well there is the Plaza Premium arrivals lounge T4 as well as the one in T2.

(it can be argued that from T5, T4 arrivals lounge is less stress to get to than T2 arrivals lounge - as you can take the perimeter bus and just sit it out, without going up and down to the underground/trains levels and then walking about underground in the central area.)

Both of these are landside - hence they are reachable by you.
You won't get airside in another terminal without a BP for that terminal.

The short answer is those are your options.

If someone was willing to spend some money, etc, they could buy a throw away ticket to get a boarding pass for a flight out of the another terminal, but you then have the hassle of getting out of departures in the other terminal, and back to the true terminal.

If someone was willing to spend over £250 on shopping, heathrow can sometimes arrange to take you to another terminal to shop. But there would still be no guarantee of getting into the lounge.