I have a couple Lennox heat pumps I want to have checked. Aside from gas
pressure and current draw, what else would they check, or should I
specifically have them check? I regularly change the filters so they
shouldn't need to check those.

I could easily check the current draw with a clamp-on ammeter myself - how
good is current draw an indicator of a system health?

Lastly, is it really a big deal to check line pressures? Should I get a set
of gauges and Do It Myself?