Just a comment Steve,
I guess it all depends on how you want to use LC and how you work. You can do all that doctf has shown, but,
for a newbie it is just not the way to go about it in my opinion. LC is a dxf importer and produces gcode based on the machining operations you want to do. LC is not a CAD program ( this is noted over 10 times in the manual).
Folks need to understand, that they need to think about all the different machining operations that will be done.
Then you can focus on defining cutting parameters to those different machining operations. Otherwise you may spend "hours" trying to manipulate chains or entities, tricking LC, or whatever, and even then, when it comes time to post you may not be able to get the operation's in the order you want to do them. Even selection of them can become a bear because of naming. Take a hard look at the manual.
Your air cleaner took around 35 minutes to draw and i was able to do all maching operations required for the piece.
This included redundant machine operations IE; after the horizontal lines where machined i would probably need to due another profile cut to remove some machining marks left by the cutter to clean things up. Very easily done by just adjusting cut depth by a few thou's.
In the end, you will have more success at getting the particular pathing more quickly, and not trying to do layout with LC which it really is not meant to
Have fun.... just a suggestion,
RICH