I guess it depends what you really want to do...
We use the tankless 12VDc Portable air compressor (AMAZON) that is rated for 150PSI but I doubt it would never get that much haha...
For us this is great for our OFF-ROAD POPUP trailer setup - Our main use is in the winter months to blow-out our water lines in the POPUP trailer water system for winterizing in a hurry. We use an adapter at the city water port where we can put compressed air into the water lines from there...
Being tankless it doesn't jump right into high air pressure when turned on and slowly builds up air pressure. This is exactly what we need for blowing out our POPUP trailer water system...
Works good for us topping off our trailer and truck tires. With its long provided air hose we just sit the the air compressor on the dropped tail gate of the truck and connect to the trailer 12VDC batteries directly. Then we can walk around to all of the tires with the long hose... The small air compressor stores great under the truck rear seat...

I suspect you may be loosing some DC POWER just plugging into a 12VDC lighter socket. May work better if you clip directly onto the battery terminals.
Roy Ken