How can I power the mAP Lite via 12VDC? Would I need a PoE injector?
It will likely be hard to find an 802.11af/at power injector that is powered by 12v.
But on the DC input this device requires 5v.
I would say: get the mAP instead of the mAP Lite, it has the 12v DC input jack that you require!
Official product brochure for mAP lite mentions
Supported input voltage 5 V (USB); > 10 - 60 V > (> PoE in > - 802.3af/at or > passive> )
So if you fetch a RBGPOE PoE injector, you can supply mAP lite with 12V. You can even use RBPOE, which is fast ethernet only, but I don’t think price difference is worth the fuss one might encounter in future when same PoE injector might get used in Gbps environment.
Interesting, the specifications page on the website does not say that, it mentions only 802.11af/at.
But then it says 10-60v which sort of hints that it accepts the old passive method as well, so that is probably true.
Sadly this is not the only specification web page which is incomplete (not to say misleading). I’ve learned to check all available documentation (which is scarce if we compare it to docs for comparable products by some other vendors) … which, of course, I fail to do myself quite oftenly 
True, but I also often see on this forum that people choose the absolute minimum level of equipment and then run into issues doing what they need to do…
Often the versions without “Lite” or “mini” in the name offer the options that one needs, and may be $20 more expensive but what does that matter when you can avoid buying and using another power inserter?
Ain’t Mikrotik a beauty … letting people make (non-fatal!) mistakes and learn from them. Learning from other people’s mistakes is largely overrated 
I love the hAP mini that I got as present at a MUM and I sometimes use it as a WiFi station to connect some ethernet device on the other desk e.g. to configure things (it is set up as a bridge to the local network).
But then i read that other people use it as their enterprise core router with failover between 2 ISPs 