Can you tie conductors together on lugs?

No, at least on the type pictured. You can only have one wire per screw. Your idea of a pig tail is exactly what you should do.

There do exist terminals that can support more than one wire, but this does not appear to be one.

Definitely not allowed!

If you want to do that, then shop for certain spec-grade switches and receptacles ($3 instead of 60 cents), which have a feature some call "Screw-and-clamp". This allows you to back-wire 2 wires under each screw, and you tighten the screw to clamp the wires.

Also note that since it's in a metal box, your switch does not require a ground wire. It will pick up ground via the screw threads and head. This trick doesn't work for receptacles unless the receptacles are labeled "self-grounding", which most of the "spec grade" receptacles will be.