I got a reply on the Mikrotik forum. The mAP Lite will not broadcast its "LAN" SSID if it can't connect to a "WAN" network. A couple people there said they use it as a travel router and just save wifi profiles for different WAN SSIDs, then factory reset it and load the saved config.

I wound up buying a GLInet one mentioned in the small router thread. I'd like to play with Mikrotik, but it'll have to wait.