Can eating brown lettuce make you sick?

It's a possibility, but as a preventative measure, you should never eat it. You can remove the brown parts and still eat the parts of the lettuce that are still green and crisp.

Lettuce turns brown due to oxidation; water will usually collect at the bottom of the bag during this process. When this happens, it becomes food for mold and that in turn can make you sick.

Of course a little browning is natural and is unrelated to mold. When preparing a salad in advance, handling the lettuce and breaking it into smaller pieces with your bare hands is recommended because using a metal knife causes the lettuce to brown even faster.

Also, storing the lettuce in a tightly closed container helps to keep it fresh.