Can I break my lease for brown recluse spiders?

First, baseboards are not going to stop spiders, may not even slow them down.

If the complex is making effort to deal with bug and spider problems, there is nothing you can do as far as your lease is concerned, they are technically doing their part.

Brown recluse will infest the woodwork, and there is little that can be done about that, it is something that professional exterminators have to handle. In your own unit, you need to take steps in dealing with them in your own personal space.

Unless you were to relocate outside the range of the recluse, you could easily wind up in a building with a greater problem than what you have now. Perhaps the best you can do is just routine cleaning with a vacuum and maybe some non toxic sticky traps along walls. A periodic inspection of furnishings and major appliances, book cases, and entertainment centers, looking for hiding places, will keep the spiders to a minimum.

Except that spiders DO come from outside. Didn't you ever read Charlotte's Web? If you haven't I'm not going to ruin the surprise, twist ending for you, but needless to say it describes how baby spiders get from place to place.

A brown recluse bite is very rarely lethal. Consider yourself lucky. If you lived in Arizona you could have tarantulas or scorpions in your apartment. When I lived in North Dakota and Colorado I used to have problems with prairie dogs in my yard. Not only do they make holes that are big enough to catch your foot in so you can fall and break your ankle, they can also carry plague. Yes THAT plague.