I have never come across a rattling liquid line before. It was knocking around pretty hard where it entered the housing. What causes the liquid line to move? A loose connection at the coil? This was one of the many problems with this HVAC system in a 100+ yr old home in Dallas.
The suction/liquid lines were not supported at the exterior either, but it wasn’t moving outside that I could tell.
Liquid line can …pulse…( think water hammer ) and that will cause a rattle where it passes close to and contacts other parts. Pulse can be caused by incomplete compression and expansion through expansion valve. This can be the result of cold weather operation. Certainly a loose part may also be the culprit however in that case there would be no cooling going on as a part on the line loose enough to rattle would have leaked the cooling fluid as well.
Don’t get lost in the expansion valve theory as expansion valves don’t compress the refrigerant they simply decompress the refrigerant they are the dividing line between the high pressure liquid and the low pressure vapor in the grand scheme of things. The unit most likely had capillary tubes as the expansion valve and there would be no movement. My guess would be a vibrating blower wheel and or blower motor on the furnace