The default shader/renderer (forget what the actual name it is called in the cauldron) is drawn always facing the screen. There are a number of different render types that can be set for the emitter, basic, additive, exclusive etc. Some of them will be basic ZX plane or something similar. These renderers will render the particle on that plane any rotation done will be perpendicular to the render plane. Or at least that is how I remember it being. Can't check from here unfortunately, will have a look back in when I'm home if no one has sorted it by then.

As far as I am aware you can only rotate on one plane and that is perpendicular to the image. So while you can set the render option to ZX (so it is parallel to the ground) and rotate the image to appear diagonal, you can't then rotate it so the image is viewed vertically as well. Which looking at your structure might be ok, but not ideal.

The reason the beam effect does not have the zx/xy plane options is that the beam effects are supposed to be made up of lots of particles traveling from the origin to the target, rather than being a single texture.

I've altered you effect as an example, adding a second emitter cause I thought it looked a little nicer. I don't think it is exactly what you were trying to do but I think it is as close as you can get currently. The rotation won't be quite right as it was just a rough guestimate. The rotation is measured in Radians of which there are 2pi of in a circle (6.28 ish).

Altered Effect: Download

I think in order to make it less obviously on one plane, you would have to essentially create the whole lightning bolt yourself using smaller individual parts; which would be quite tricky.