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According to LotFP player core book (page 7), when a character levels up, it's maximum Hit Points are incremented by a random variable:
For determining Hit Points at level two and higher, it is simply the shown die roll plus the Constitution modifier.
Some creatures (such as vampires as described in A red and pleasant land) can make a character lose a level. In this case, it is admitted that the character lose a hit dice. Does this affect its hit point maximum? if so, how?
There isn't really an official procedure for level drain or level loss; level drain isn't mentioned in the Grindhouse edition rules, referee book, or the more recently updated Rules & Magic. In fact, with most games in the retroclone genus that Lamentations of the Flame Princess comes from, there's no process mentioned for reducing hit point totals from level drain, although it's assumed that it exists. That being said, there's a few house rules I can suggest.
Roll a Hit Die for Level Loss
Roll an additional hit die as if you were gaining a level including applicable modifiers such as Constitution; subtract this hit die from both your current and maximum hit points, reducing your maximum hit points to a minimum of your class's minimum first level hit points. If this roll would reduce your current hit points to 0 or less, instead it reduces them to 1 (if you're feeling kind). If you're losing a level where you would have gained a static increase (levels 10 and above), you lose that static increase. This is like an inverted process of the procedure for gaining hit points on level increase on page 35. This has the advantage of being a very fast process, but will usually give the character greater or fewer hit points than they originally had at that level. If that bugs you, I'd suggest this other process:
Keep track of hit points at each level
If you (and your players) have the foresight to keep track of their maximum hit point totals at each level their character has, you can ask them to reduce their total to a given level when they are level drained. This process is identical to the one suggested in Lino Frank Ciaralli's answer. The downside to this is that if you haven't been doing it all along, it's not really possible to start now, and it does increase bookkeeping by quite a bit. In the event of magic effects permanently increasing hit points or granting an extra hit die (as happens in certain LotFP adventures), it may become even more complicated.
Hopefully either of these methods helps; if worst comes to worse, you can also turn to the LotFP forums and try badgering an answer out of the author.
When I know that I'm throwing creatures like this at players, I ask players in advance to track their rolls for each level if they're rolling HP. That way if they lose a level, they revert to the last levels HP total until they regain the lost level.
If the players are NOT rolling their HP and just going with averages, then you just subtract an average and it's corresponding +CON and any HP from feats.
Now, if you really, really hate dealing with level loss mechanics (it's really time consuming), you can use an alternate that I like, which is temporary negative hit points. They can only be removed through special magical means, but effectively do the same thing without having to de-level everything with it. It's fast, simple, and effectively reduces their max HP. I phrase it as a persistent ability so even if you have a heal that gives them up to 50% of their max HP as temp hit points, you can rule that the negative temp hit points applies before the 50% max so that they don't game the system against you.
