What Allenby thinks he hears that makes him so uncomfortable is that Lawrence was uncomfortable with killing the man because he had a sexual relationship with the man. It is considered fact that Lean inserted a lot of gay subtext in LoA very subtly [to get past the censors of the day], and it is subtle enough that it gets past even modern audiences. This is all based on historical record which has records of Lawrence befriending a young Arab boy in Damascus before the revolt and living with him for a length of time in the same house. IIRC, everyone in the neighborhood knew he was doing it but no one said anything and he never denied it. The boy was killed before Lawrence returned to Damascus after the revolt and the opening poem in Seven Pillars is widely considered to be a dedication to him and seems to imply that Lawrence did the whole thing just to be able to get back to the boy and free him from the Turks.