That type of battery is designed to put out a large amount of current for a short time,
typically 30 to 60 seconds. As such, it won’t last very long before it “goes dead.”
(that’s why your car won’t start the morning after you find you left the dome light on the night before)
If you don’t need a “long term” solution, the mower battery would work fine. By long term, I mean
more than just a few hours. e.g. overnight, or a full day or more.
Ideally, you’ll want a battery designed to put out a comparatively smaller amount of current for a much longer interval. Deep Cycle Marine batteries come to mind here, but they fare only a bit better than the
“starting” batteries do. A trolling motor (fishing) battery would be a better choice. Golf cart batteries
would be even better yet.
I bought a USB DC-DC converter similar to the one you linked to:
but it was a disappointment. With 13.8 V at the input, the output was ~4.5 V.
That was with a 1 Amp load, which according to the device’s spec, should’ve been no problem.