GameArts owns the rights to the games. Gungho owns GameArts. Apparently it was hard, but Sega managed to get permission to include the games in the Japanese version.
Working Designs owns the rights to the English localization of the Lunar games on Sega CD & PS1. Working Designs is long defunct, but apparently Vic Ireland still owns the WD rights. According to a second-hand source (who got perma-banned on this site), Sega contacted Vic, he though their licensing offer wasn't good, and so he didn't agree to letting them be on the Genesis Mini. They're JRPGs and Lunar:EB is a good 30-40 hours long, so re-translating them just for this would be quite the expense, so they're not on the Genesis Mini.
Since this is all second-hand, I'd be relunctant to lay blame at either party's head. I'm still incredibly depressed it didn't work out. I like Lunar: Eternal Blue more than Chrono Trigger.
I really wish Gungho would do something with Lunar, but last I checked (I was friends with somebody at the company, and we tried to get permission to make a spin-off/sequel a few years ago), the higher-ups at the company don't view it as an IP with relevance these days, and so it sits dead.