If I'm understanding you correctly, you might want to recheck that because I use a propane tree when I go camping and I'm able to run a lantern, bbq, and stove off a 20 lb tank with no issues. The first time I tried it I ran into the same issue, no/low gas, but after some research; safety valve.
Texsport 2 Piece Propane Distribution Tree with Outlets to hook up 3 Propane Appliances to One Tank, 30 inches https://smile.amazon.com/dp/B003ZZC000/ref=cm_sw_r_apan_glt_fabc_CAMDCHZ0XHVGMPK2F6JT
Here is the lamp: Texsport 2 Piece Propane Distribution Tree with Outlets to hook up 3 Propane Appliances to One Tank, 30 inches https://www.amazon.com/dp/B003ZZC000/ref=cm_sw_r_cp_api_glt_fabc_X63Y3HB2WMS27GMPR8DJ
Good luck on your off the grid cabin 👍
Item | Current | Lowest | Reviews |
---|---|---|---|
Texsport 2 Piece Propane Distribution Tree with O… | $36.11 | $36.11 | 4.0/5.0 |
^Item Info | Bot Info | Trigger
Not op, but this might help. Search "propane tree", there's several variations. https://www.amazon.com/Texsport-Propane-Distribution-Outlets-Appliances/dp/B003ZZC000