OneWorld Lounge LHR
 

Does anybody know if there are any lounge open 24HRS at LHR...

Reason arrive midnight and leave 6AM... so not sure if want to do the hassle of checking into a hotel...

Thanks...

Dont believe so.

Information regarding OW lounges, including operating hours, can be found here:

http://www.oneworld.com/ow/ffp/lounge-access/search

Choose "London (Heathrow)" in the location pull down menu. I believe this will confirm chanp's direct answer.

Regards

So, that would be a "No", though the link is helpfu.
For the OP, there is a Hilton attached to T4. Whether 6 hours is worth it, is up to you, especially since you have include de-boarding, boarding, immigration, and security times.

Other options...
 

There's also a Yotel in T4 (Groundside) which rents 'cabins' by the hour. It's cute and reasonably comfy. With a six-hour overnight connection, you can actually get a couple hours of a nap and won't have to shell out for a whole night's hotel or leave the terminal.

Since no OneWorld flights are in/out of T4, I wonder how convenient the Yotel or Hilton offerings really are. I'm not aware of any trains from T5 to T4 --- are there frequent buses late at night/early in the morning? Re T3 - T4, I wonder what time the Heathrow Express shuttles from T123 to T4 stop, or whether this also requires a bus (or expensive taxi) after midnight?

Due to LHR curfew there are no 24 hour lounges.

Some of the public buses to nearby suburbs, which stop along Bath Road (free) where the airport hotels are, run 24 hours. The buses leave from central bus station. Some of the airport hotels are only GBP19 + tax.

The hoppa bus (GBP4) isn't 24 hours but runs until fairly late and resumes around 0430 IIRC.

Do you have any recommendations?

Afriad you're out of luck. But if you're inbound from BCN as I believe your profile indicates, you'll probably spend an hour getting your luggage, and then hike over to... T5 or T4? Either... you'll spend an hour on the bus, just about ready to spend an hour waiting for checkin to open, and then, the lounge will open... depends where you are heading for, but the BA T5 lounges will open early if you are on an overnight T5 lounges and most vitally champers is there around the clock.

Having said that, I wouldn't recomend it: you'll feel a bit lousy after a night awake: if you can grab 3 hours in the Yotel horizontal, it is worth it.

Just let us know where you are heading from and to.

local buses to hotels
 

The Ibis on Bath Road isn't bad, I stayed there once. I like the Holiday Inn on Sipson Way (beware, there are 3 Holiday Inns in the area!) - this is one of the closest hotels to the airport, by the North gate. These are not as cheap as GBP19 I'm afraid.
As to getting back and forth, the Hotel Hoppa works but is slower and less frequent than the public buses and is ridiculously expensive at GBP4 each way. The local buses are free within 1 mile of the airport - look at this PDF map of the buses around Heathrow to work out which one to take, from T1/2/3 (or other maps for T4 or T5)
The local free buses are more frequent than the Hoppas until about 19:30, then they're about the same. Ah, if you need nightbuses, look for either buses with route numbers starting N like N9, or look on the map key for the buses with a 24hr schedule.