Avalugg's Special Defense is pretty pathetic, you don't need a SE move to deal with it.That core obviously has trouble with Avalugg unless Lilligant runs HP Ice.
The best Hidden Powers for Lilligant are either Poison (SE effective against Rock and Ground) or Fire (stronger in the sun, SE against Rock and Water). Considering the prevalence of Groudon and the fact that Water-types are weaker in the sun, I'd probably pick Poison. Which is why Venusaur is a better sun sweeper: it just happens to have the perfect STABs for the job.
The sad thing is that there would be perfect counters to OU sun teams, but they all happen to lose to that monstrosity called Groudon.
Abomasnow is perfect to neutralize the sun, because it can switch into sun setters. Sadly, it's weak to Groudon. Gogoat can counter pretty much any sun sweeper, because it's immune Grass and it resists Fire, Venusaur's Poison, Charizard's Flying, and Volcarona's Bug. Sadly, weak to Groudon. And so on.
And sun was already the best weather in Inverse before the introduction of Groudon, I did try it pre-Pokébank. Grass happens to be one of the best offensive types, sun neutralizes Grass-types' weakness to Water, and sun setters have an advantage against any other weather setter not named Abomasnow.