Should I use aluminum and copper to make woodworking tools?

In short, copper and aluminum are soft metals, and you'd need to consider the quality of the casting and the metallurgical treatment of the tool as well. It sounds like a fun project, but watch out for potential catastrophic failure of the tool.

The first metal tools used by man were copper and copper alloys (bronze and brass). The main problem with these metals is that they are much softer than steel, thus holding an edge for less time and also in a greater risk of bending the tool itself (and not just the cutting edge). Aluminum in pure form (i.e. not an alloy of aluminum) is even softer than copper.

A further issue is with the quality of the casting. How well can you create a uniform alloy and then cast it so that the finished tool will not have any voids or weak spots due to poorly mixed alloy or other flaws? Any such issues will impact the strength of the tool.

Finally, there is a large difference in metal hardness with different treatment methods after the initial casting. Metals most often can be annealed (softened), tempered (toughened) and hardened. A good tool steel alloy can be hardened to twice (or more) the hardness of the original steel.

Now for some numbers (comparing different hardness scales is difficult, but just so that you have the right impression):

1. On the most commonly used Rockwell hardness scale, steel and copper/aluminum don't even use the same scale (there are HRC for steels and HRB for softer metals). Typical tool steel is about 60 HRC, while brass (which is harder than pure copper) is about 70 HRB. However, 70 HRB is much softer than even 1 HRC.
2. On the Brinell hardness scale, tool steel has a hardness of about 700, while aluminum is 15 and copper is 35. And just for comparison, hardwoods have a hardness of 3 to 7, so your aluminum tool might be only slightly harder than the wood it is cutting. I would imagine it would be like cutting pine with an oak chisel. The most dense hardwoods are probably even harder than copper (woods like Lignum Vitae).

Finally, since you are asking about tools for a lathe, I would be very careful. Lathes exert a lot of force on the turning chisels, and it might cause a catastrophic failure, especially if there is some flaw or void in the casting. The tool might snap suddenly, sending shards flying at high speed.

At the end, it does sound like a nice project to try out, but I would start from tools that don't have such a high risk of damage. A marking knife would be a good start - it will allow you to assess the edge holding capabilities of the metal you are working, and would be pretty safe should the tool suddenly break. Then I would step up to small hand chisels (not for lathe work) and then progress from there if results are satisfactory.