Isn't this an instant win combo with Lab Maniac or Barren Glory or some other degenerate combo which involves putting things on the bottom of your library?

A lot of things combo with Laboratory Maniac. It doesn't really combo well with Barren Glory since it doesn't get things off the table, which is the tough part of the Glory.

Not sure what the 'degenerate combo which involves putting things on the bottom of your library' is. You'd still have to exile the rest of your library just to play that card over and over. The end result would need to be on par with Eternal Dominion for it to be worth it (in a strictly Spike-y way of 'worth it'.)

Which isn't to say the card isn't Bonkers T. Bobcat. Since most games use less than 30 cards out of a 60 card deck, this card roughly represents a gain of 40 life for with few negative ramifications (since you would only gain the life if you were about to die.) The card is admittedly trickier if your opponent has a Demystify ready... but you could probably sneak 20 life out of this card before it goes to the bin without worrying too much about being decked.

I'd say "Gain 1 life for every two cards" but people don't like 'drawback' mythics that are balanced. Tricky problem.

I've personally been thinking about the subset of cards with 'Whenever you gain life' with which this is quite bonkers with. Hence the edits. I might have erred on the side of too much caution with the "until ~ LTB" clause.

Gaining ~40 life for doesn't sound that impressive when you think about it competitively. Life gain does have the problem of stretching out games though.

Lab Maniac has always been questionable in multiple ways. In this case, I would say you are still better of with Leveler and especially with Puresight Merrow + Paradise Mantle. Regardless, if Maniac were to be truly problematic, I would say the issues there lie with the design of Maniac more so than with this card.

Yeah, life gain from a strictly competitive point of view is weird. I think I remember Wizards doing an informal questionnaire of pro-tour players, asking how much life gain is necessary for them to think about playing a one mana instant that only gained life. Results varied, but I think the average reasonable starting point was 8... which is clearly not Magic baseline.

Personally speaking, I prefer to pretend that the current life gain model that we use is the right one. Mostly, because I assume Wizards has playtested other options, and I have not. But I definitely understand the desire to slide the life gain scale up to a more competitive level. As long as you're okay with the idea that playing this card on round 5 demolishes red burn and suicide black. Not every fake Magic set needs to have the same metagame parameters.