I find:

$ ./pants kill-pantsd && ./pants --enable-pantsd list 3rdparty/::
$ ps -ef | grep pantsd | grep -v grep
jsirois    77290     735  5 15:55 ?        00:00:03 pantsd [/home/jsirois/dev/pantsbuild/pants]
$ lsof -p 77290 | wc -l
lsof: WARNING: can't stat() tracefs file system /sys/kernel/debug/tracing
      Output information may be incomplete.
386

So a fresh pantsd starts with ~400 open files. That presumably grows over time. Of those 386, most are lmdb:

$ lsof -p 77290 | grep .cache/pants/lmdb_store | wc -l
lsof: WARNING: can't stat() tracefs file system /sys/kernel/debug/tracing
      Output information may be incomplete.
288