I've always thought of Thunderbolt and Lightfoot as buddies, and never considered their relationship as a father/son one. So, it struck me as pretty funny when I read the novelization where Lightfoot called Thunderbolt "pops". But, when I think of it more... Thunderbolt is a father-figure to Lightfoot. He's wiser, mature, and more cynical, while Lightfoot is still so full-of-life, excited by everything, almost in a child-like way, and reckless. He seeks and respects Thunderbolt's advice, and in his paternal role, Thunderbolt also tries to protect Lightfoot.
I don't agree with Gallafent that their relationship is limited by a generational gap. I'd offer that the generational gap may have brought them closer. Lightfoot didn't have a father, Thunderbolt didn't have a family. I think they found in each other a lot more than most friends ever do.