I tried to think about it but I don't understand what I did differently in NG+ to get Lautrec instead of Solaire.
I also helped a lot of people fighting the Gaping Dragon and ALL of them summoned Solaire!
Actually, I don't remeber in my first playthrough which sign I saw, because I didn't summon any NPC.
This is what I did: I freed Lautrec in Undead Parish and talked to him a couple of times in Firelink. I don't remember if when I went to the Depths he already killed my fire keeper.
Yeah I know I should probably kill him as soon as I meet him, but I actually enjoy slaughtering him and his friends in Anor Londo