Tengen Toppa Gurren Lagann, Shin Getter Robo Recommendations
Getter Robo is by far the biggest influence on TTGL, as admitted by the staff and as evident in the show. New Getter Robo isn't the best of its franchise (the Getter Robo Saga manga is), but is likely the most solid and accessible of the animated incarnations.
TTGL's main inspiration was Getter Robo. Like TTGL, it has drills, a lot of gattai, and an energy that is kinda similar to spiral energy known as the getter rays. Reading the manga is recommended as well. Both Kamina and Ryoma are the greatest examples of traditional hot blooded heroes. New Getter Robo is a remake and sticks closer to the manga.
New Getter Robo is a 2004 remake of the original 1970s Getter Robo which Tengen Toppa Gurren Lagann is heavily based on. If you can handle the retro mecha and character designs (and if you can't, you're a philistine), this is an excellent series to check out and see where the combining mecha sub-genre has its origins.
Almost obvious and self-explanatory. Both have mechas. Both have badass heroes. Both have FIGHTING SPIRIT.