Question: This is happening on two computers. Are both computers slow or is the software itself slow?
Problem: Slow (Really Slow) at drawing sketch line.
Difference from previous models: Lots of lines in a sketch trying to model 4 X 8 sheet of expanded metal mesh
It is definitely the software. Fusion 360 does not like complicated sketches. If you can sketch a smaller section (1' x 1') and then do a rectangular pattern after it is extruded to get your 4 x 8 sheet, it may be easier to achieve the result you are looking for.
What Todd Durbin said.
Might also recommend using simplified model inside your assembly.. if in fact, you're building one.