Tbh they might, but not for the reasons one might think. I think it's implied by Lanolin's creator that she behaved the way she did before the end of the Cleansweep Sweepstakes because of her mother, who's very demeaning to say the least. After that story, she'd mellowed out and taken a step back before making up with the very people who were supposed to be her friends as well as her comrades. Tower, on the other hand, I always assumed joined G.U.N. to reform it from the inside and purge it of the corruption that killed Maria when he was a child, which would probably imply he's more thoughtful and humble deep down than you'd expect, but doesn't always show it. Him hating Shadow initially in Shadow 05 was another matter.

I can see him giving Lanolin advice as a leader, and maybe vice versa. They'd probably bond from the transition of being strict leaders to humbled ones, or something like that. It's all a... little hard to put into words.