I read an interview with a famous pianist (I can't remember which one! someone marvelous) who recommended that every pianist spend two weeks each year playing with only the left hand, because it is such a weakness for almost everyone. Scales, left-hand pieces, and--mainly-- their own repertoire, but just the LH parts.
I think all the previous suggestions are great, and I have another thought to add: Part of what our hands do is what they've practiced doing, but I think, even more so, that physical coordination and prowess is the brain or imagination sending the clearest possible signals to the nerves, which makes the hands sort of self-coordinate. So my thought is to take one piece (or section) and memorize the whole LH part. Learn it as its own piece, without thinking about the RH or melody at all. If you already know the music, it's diffiicult to tune all that out, so you may have to try this with a new piece you've never heard. When people tell me they can't memorize, I ask them if they can sing or play the melody of their piece. "Oh sure," and they do it. Then I ask, how does the LH go? They have NO idea. Your question isn't about memorization, but I think both issues involve the same areas of comprehension and attention that tell our hands what to do next, and somewhat automatically they do it.