Door lock relay needs higher amperage - what relay to use?
I hear you, the selection can be overwheming.   

Start with the coil voltage.  It must match what your controller outputs within 10% or so, that's mandatory.  

Next look at coil amperage.  You cannot exceed your controller's output, and since relay coils are inductive loads, I'd aim for more margin still, e.g. 200ma or less.  

Next look at the contact voltage rating of the relay contacts, though that won't be a factor at 12V.   Your door solenoid is an inductive load, and those love to arc, so the more DC voltage rating, the better.  (Not to be confused with AC voltage rating: because AC current often goes to zero, this tends to snuff arcs.  DC doesn't have this advantage, so a common relay rating is 250VAC or 28VDC.  Yes, a factor of 9.)

Next look at the contact current.   I like to go by a 2-3x margin for a resistive load, and a lot more for an inductive load like this. For this 750ma load, 10x is 7.5A and that is not excessive especially because it won't cost you much more.  

When I have a wide selection, I look at packaging.  Does this relay solder onto a PCB? Does it use blade terminals? Screw terminals? Loose leads? A connector? How does it physically mount?  90% of electronics is physical. 

Next I look at stocking.  How many does the distributor have in stock?  I like to see hundreds in stock - a relay they have 3 of with a 12-week backorder is a bad choice.  

Last but not least, I look at price.  

You'll find you can obtain relays with 20-30 amp contacts in the US$3 range, barely more than a 1A relay.  While that seems like wild overkill, it's not with an inductive load.