I have family in Warren, and I've driven through Lodi many times just to get off the freeways. And, traditionally, to buy Oreo's (long story).
Looks like the mag lock has two coils for operating on 12 V when connected in parallel and 24 V when connected in series. And it has a SPDT (form C) status switch. So far, all the right pieces.
The LA500 drawing indicates that it can drive a maglock directly if the lock has its own external power source. The LA500 is acting as a switch, not a power source. Does it have a rating for the max voltage/current/power the maglock output driver can handle? Also, is the maglock AC or DC powered? A photo of a wall wart is not enough information.
ak