Limited lives is objectively funner because there are higher stakes involved than just respawning and running at brothers with whatever you have. It forces you to brown townyze your hand and understand which foes are easier to fight and which ones aren't. Of course, that's only provided that the game is truly random and some people can actually spawn with booty weapons.
Best way I can think of is to meticulously design your maps so they incorporate all playstyles (cqb, long range, acrobatic, airshot, splash, etc) and use a roster of equally balanced weaponery similar to tournaments. Then, when you get a random hand, you won't be limited by how bad the guns are but rather your lack of skill or versatility with that set of weapons.
Some people might get a sniper and a shotgun, a great pair that can dominate most of the playing field, while some people could get like, a shotgun and an assault rifle, which restricts them to mid-close range. Though it's randomly chosen what weapons you get and some will get a better chemistry of weapons, you can still use your lack of versatility to focus on one playstyle that round, making you just as effective. While the sniper enemy will have long sights of the map, your shotgun wielding ass will have to adapt to flanking the sniper and utilizing cover to get in close. Then you level the playing field.
This kind of randomizer is incredibly dull but well balanced. You could spice it up by adding wacky weapons that are still well balanced, but for the most part the goofy slapstick randomness has to be sacrificed for the much needed balancing
