Using list_id to search with Life Lists works as intended, it’s just that the intended behavior isn’t really what most people expect or want.
You can get more background info on how iNat counts taxa in Life Lists and elsewhere here, but the short version is that k_a_m’s Life List currently includes a number of species/genera, but also 3 taxa above genus: Order Passeriformes, Order Araneae, and Subphylum Angiospermae.
If you compare the results of a search on list_id=3177272 to a search just of those three taxa, you find that almost exactly accounts for what’s returned (the list_id gets a few more from the genera and species it additionally has).
If k_a_m is willing to get rid of the high level taxa from the Life List, then using it to search should work as I think people expect it to. The way to get rid of these high level taxa is either to manually delete each one (using the little x to remove from list) or to change the Life List rank restriction, reapply list rules, and reload from observations.
Manually removing them allows you to leave genera, but you may get more issues in the future as you add new observations. Changing the list rules means it will only ever contain species/subspecies and should be useful as a search parameter.
Edit: it’s probably worth noting that lists are about to get a re-vamp. I don’t know how that will affect these instructions. Also note that reloading your Life List is computationally intensive, so try to keep it to a minimum, especially if you have a lot of observations.