It needs to generate a waterfall or otherwise disrupt the surface to aerate the nutrient. If you can get it to do that, it will aerate just fine.

by waterfall, do you mean that the water has to create a splashing effect(the one where I see bubbles) or is it okay if it falls gently?

What I have now is an 8inch deep 1x2' tank with a raft above it. I have a water level pvc tube that drains down to my res tank when water goes above it. but it doesn't splash where you see bubbles, it just falls gently because the water draining at any given time isn't that much. is that enough to provide enough aeration for 4 lettuce? I'm using those 3/8" tubing to bring up nutrients to the raft tank, so you can imagine that is also as much water draining down.

The water needs surface agitation for more efficient oxygenation.

Why are you staying away from an air stone?

Here is a link that might be useful: My Indoor Growing Adventure

you could either shorten the overflow pipe so the water falls further before hitting the reservoir nutrient or you could modify the feeder line (to the raft tank) to create a waterfall in the top tank.
Is the "in" line on the opposite side of the raft tank from the overflow line? And does it open into the tank at the bottom?

@ halfway
Mainly to save electricity. Ours is expensive here

@grizzman
Yes its on opposite sides.

Pump the water into a pvc spray manifold. It's just pipe with holes drilled in it. A 1/8th" drill bit will work. The holes are on the underside of the pipe and the water will flow through that. It should sound like a lot of peeing.

Also, air pumps aren't really energy suckers. You wont even notice the difference in your bill i'd bet

is there a cheap way to measure dissolved oxygen?