Anodizing Aluminium LM24, A1060 -- is it possible?

A. That depends mostly on your definition of looks good. Anodized cast will never look as good as a machined wrought alloy.
Sometimes you would get an excellent casting, but normally it was from the lowest bidder. The same with extrusions.
Have you looked at powder coat and some of the two part paints which have far better scratch resistance than sprayed paints.
Even if you go to a hard, plated finish, if the initial casting is garbage, the plated part will be shiny garbage.

"The Surface
Treatment &
Finishing of
Aluminium and
Its Alloys"
by Wernick, Pinner
& Sheasby

(note: this book is two volumes)

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A. Sheasby and Pinner show LM24 as: 8% silicon, 3% copper, and 1.3 % iron. They say it is recommended for protective anodizing as "moderate", not good, not very good. They say not recommended for dyeing except darker colors. They say unsuitable for bright anodizing. End of S & P.

Since you anodize aluminum and not the silicon on the surface, it is important that your preparation removes as much silicon as possible before anodizing - you must use a fluoride, maybe not HF but ammonium bifluoride. In my book, for die cast I recommend 50% nitric with one pound per gallon ammonium bifluoride. Try the process in a small way before setting up. And be aware , that the cooling rate and the recipe range of the LM24 affects the amount of silicon on the surface.