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Yea, you could shoot 120mm negative film (black and white ideally) with your lomo, develop that, and project the negatives onto your cyanotype emusion (assuming you have a projector / enlarger that takes 120mm) - this will give you a positive cyanotype image.
If it really is the cyanotypes you're after I'd probably rather shoot with a digital camera, probably edit the pics into some nice and proper contrast-y black and white images, and print those on overhead transparencies (acetate sheets) - you can then lay those flat on your cyanotype emulsion coated paper or whatever, maybe put a piece of glass on top, and put that under the sun / UV lamp..
not too versed on photography here; can I take 120mm photos on my lomo, have and them made into slides?
the goal is to project them on some big pieces of card stock that i'm going to coat with cyanotype compound.