The triggered ability will consider the total amount of life you've gained that turn, not how your life total has changed. For example, if you start the turn at 10 life, then gain 5 life, and then lose 7 life, you'll distribute five +1/+1 counters, even though your life total is now lower than it was at the beginning of the turn.

If some, but not all, of the creatures are illegal targets as the triggered ability tries to resolve, the original distribution of counters still applies and the counters that would have been put on illegal targets are lost. If all of the creatures are illegal targets, the ability won't resolve.

Gaining more life in response to the triggered ability won't change how many counters will be distributed, nor will it change the distribution.

You may choose no targets if you want. In that case, no +1/+1 counters are put on any creature.

As each end step begins, if you haven't gained life that turn, Lathiel's triggered ability won't trigger at all. If it does trigger, you choose the targets and how the +1/+1 counters will be distributed as you put the ability on the stack. Each target must receive at least one +1/+1 counter.