I don't know why combat doesn't fit Lovecraftian fiction. Just because Lovecraft wasn't really good at writing action scenes — well, he wasn't really good at writing fiction in general and action in particular — doesn't mean it's out of place. Lovecraft did pulp fiction after all. Many board games with a Lovecraft theme feature combat and still retain the dark and oppressive atmosphere, although in this case combat is only one option available and depending on the enemy might best be avoided in some circumstances.
Shadow Over Innsmouth gets actiony once the denizens try and get a hold of the protagonist.
However I'd definitely like to add in the vast majority of Lovecrafts fiction, the protagonist is lucky to escape with their lives (and usually not their sanity), or is touched by the old ones (or other monstrosities) in some horrible way, like the protagonist in Innsmouth.
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