Why does the genitive case turn my 'u' into an 'o'?

I'm a grammar-focused learner trying to internalize noun declensions, but the morphophonemic changes in Lithuanian noun endings are killing my flow. I grasp the basic rules for nominative vs. accusative, but once I get into genitive plurals, the stem changes feel random. Does anyone have a mental framework for how these vowel shifts work, or is it just a matter of brute-force memorization?