mAP lite not responding on Wi-Fi -- arp?

Well, now the "outward facing entity" (the bridge) has an IP address and should respond to ARP requests.

In any case having the iP on the bridge is advised.

Another thing that you may want to try (as it is usually advised) is to assign manually a MAC to the bridge, that would be Rule #6 :
The twelve Rules of Mikrotik Club
but I doubt it can be related.

Before a support ticket, I would try downgrading to an older release.

You don't mention it, but did the thingy work with a previous release and stopped working when you updated it to 7.21.2 or this is a new install that has never been tested before?

For a configuration as simple as yours, you have no real advantage in running 7.x (if not some added slowness and more storage used), I would downgrade to 6.49.19, but if you want to remain on 7, try 7.19.6.

The:

/system routerboard settings set auto-upgrade=yes

is IMHO "pure folly", that would be Rule #10.

I don't understand (but this is probably just me) how the device is used (Ap, station or something else) if no ethernet port is configured/connected and the bridge has only wlan1 in it.