The bigger question is if you can get into T4 after clearing customs at the TB Intl Terminal (on BA) since your flight to LAS (on AS) leaves out of T6, and if you can get into T4 then will you have enough time to get to your T6 gate?
OP has a few choices after clearing immigration at TBIT. 1) reclear security at TBIT and then take the tunnels to T6, stopping at the Flagship lounge at T4. 2) Walk outside to the right to T4, clear security there, visit the Flagship lounge, then head to T6 via the tunnels 3) Walk outside (or shuttle) to the right to T6, clear security there, and just visit the AS lounge there. Unless time is short, 1 or 2 should be no issue.