Seems like a good start!
From my previous experiences with parser-based interactive fiction, I generally expect "inventory" or "inv" to list what I'm currently carrying. It's also fairly common to support abbreviations for directional movement: {n, s, e, w, u, d} for "north", "south", "east", "west", "up" and "down" . It's very uncommon for navigation to use anything other than those directions, half-increments (northeast/ne, southwest/sw, etc), and very occasionally "enter PLACE" or "exit PLACE".
You can use the "in" or "like" primitives in Lil to check whether a string is one of several alternatives; "in" looks for inclusion in a list or dict keyset, while "like" looks for a glob pattern where "*" is a wildcard:
verb:"north"
verb in ("north","n")
1
verb in ("east","e")
0
verb like "n*"
1
verb like "e*"
0
It's also a very important convention for room descriptions to clearly indicate the directions a player may exit, unless there's a reason to obscure it. So far as I can tell, the only way to discover the door in your room is to attempt (based on intuition) to go "down".