What you should do is turn the red lightning effect into a layer mask.
- Create a new layer, fill it with black
- Add a layer mask to this new layer by either clicking the Add layer mask button on the Layers pane or using Layer > Layer Mask > Reveal All
- Copy your (flattened) lightning artwork to the clipboard
- Open up the layer mask editor by Alt + Clicking the "Layer mask thumbnail" on the Layers pane. (It's the white box next to right of the "chain").
- Paste in your copied lightning artwork. It will turn grayscale, and that's okay.
- Invert the lightning artwork with Ctrl | Cmd + I
- Exit the layer mask editor by clicking another layer on the Layers pane
Following those steps should give you the following result:
It's not perfect because your black background in the original image was not
#000000. We can correct this by adjusting the levels (Ctrl | Cmd + L) of the layer mask and setting the white point to the background (the white eyedropper icon).
Doing so gives me the final image below that you can use to overlay on any color:
Overlaying this on blue would look like this (ignore the text since I don't have the separated layer available):
JSFiddle demo (with bonus animation in Chrome)