I am generally applying to lecturer/post-doc/assistant professor positions right now and the laboratory I am interested in has two positions opened and they are closely related in terms of research areas. I am curious whether to apply both at the same time with different cover letters stating why I am suitable for each position or would it look bad and desperate rather than interested if I do that?
It's fine. A lot of times the divisions are pretty separate profit (err...cost) centers. I've also seen people apply to CRD and an SBU also at conglomerates. It's usually fine. Just let them know if things get serious with both of them (invited for visit, say, or for sure competing offers). They won't want to negotiate against each other and one will likely bow out. You should have a preference at that time to control which direction you want to go, rather than letting them make the call. But this only applies when things are at a later state.
If you are just prospecting, spread your availability wide like tree pollen. Ideally, you will have some competing offers that are completely outside the given national lab as well (so you still end up with multiple offers).
P.s. (in answer response to a comment above) I would not feel bad about HR seeing resumes that differ slightly either. Go ahead and tailor the resumes versus the opportunity. Obviously your name, etc. should be identical. And use the same format. But if you have enough experience that you can emphasize computer work for the computer position and lab work for the lab position, that is fine. Don't misrepresent yourself. But respond to their stated needs. That is normal. I would also add that the likelihood that they end up on the table together is low. Even if you go through a central system, they will probably be presorted by job posting. In any case, as long as you can look at the two documents and see that there is not a lie, you're fine. Emphasizing Aishness for A and Bishness for B is not wrong. And in fact, HR experts will tell you to do that!