What of the following is right?
"We need to find out..."
- "...how to lower the costs or how to produce more."
- "...how to lower the costs or to produce more."
- "...how to lower the costs or produce more."
If you want to be clear, only the first one will do. The other ones could be misinterpreted as We need to find out how to lower the costs or need to produce more.
I agree with Guffa. You want to have a parallel construction, but unless you repeat the "how to" part, it will be unclear which parts are parallel.
This sentence makes it clear that the "how to" parts are parallel:
The parallel in these sentences could be "to find" and "to produce":
Alternatively, you could clarify the parallelism in the last two constructions by using "either":
Disregarding grammaticality, I don't like any of OP's possibilities. Better would be...
...how to lower costs or increase production.
...which juxtaposes the two alternatives more clearly.