How to pasteurize lacto-fermented hot sauce?
According to the US FDA, normal pastuerization for fruit juice would be 160F for 6 seconds.  This should be easily accomplished in a hot water bath; just heat up the water to 160f, and dip the bottles.

However, a fermented sauce made with chopped peppers has poor circulation compared to fruit juice, and you are heating bottles rather than passing the liquid through a narrow, heated pipe. So more time would be required for the heat to penetrate, possibly as much as 5 minutes.  I can't find specific guidance for something like a chopped pepper sauce.

This would pastuerize the hot sauce, but not make it shelf-stable.

The criteria to bottle it, as mentioned in the comments, is how acidic the sauce is after fermentation, so you should add some form of Ph tester to your list of equipment.  If the acidity is 4.6 or below, then a slightly hotter hot water bath (say, 180F) for a few minutes you could not only pastuerize it, but make it shelf-stable.