It’s been a while since I operated the L1011, but I seem to remember the following.
The L1011 APU bleed output was sometimes marginal to start the RB211 engines especially in hot and high conditions. Bleed pressure available to crank the engine starter was typically 1-2 psi higher for No 2 engine than for the other engines. We were told that this was due to lower duct pressure losses resulting from the shorter length of bleed ducting between the APU and the No 2 engine. After No 2 engine was started, engine bleed pressure (much better) could be used for starting the wing engines.
Therefore, we normally started the No 2 engine first.