I'm aware of only two 1/28 scale after market versions of the Lewis gun and they're both PE.
I plan on mounting it on top of the wing so it should look authentic.
Looking at photos of the PE's, both look like the handle part (which looks like a pistol) has no depth.
Is the handle in the finished gun actually the depth of the PE sheet?
Could I get away using a 1/32 scale Lewis?
Thank you.

Those PE guns are designed to be glued to plastic card and then sanded to shape so the PE part has depth added to it. You'd use tubing to create the barrel for obvious reasons.

But there is just one handle for each gun.
So only one side would show the PE.

The idea is to glue plastic to both sides (one side at a time, of course) to get the 3 dimensional shape. Here's a picture of similar guns done in 1/48

You can easily see the combination of brass and plastic which makes up each gun.

In 1/28 scale Tom's Modelworks has a British gun set.

Tom's Gun sets