It depends on your definition of "a lot", but certainly we have texts from pre-Spanish times which have been deciphered and, together with other evidence, give us a fairly good picture of who these people were and what they did believe:

Alright then. I guess it is highly implausible.

Come to think of it, the bigger problem isn't what they wrote. It's what language they wrote it in. I assume it's clearly not anything that decedents of Hebrews were likely to use. From what I understand of the Book of Mormon, the Lamenites had their own religions, so finding plenty of non-Mormon stuff isn't too suspicious, but their languages didn't completely change.

We'd expect to find all kinds of written texts, and ruins of cities with inscriptions, statues, temples, tombs, etc. All the kind of stuff that this type of civilizations leave behind.

Haven't we? Is there some reason all the stuff we find about the Incas and Mayas etc. don't count? Besides the writing, which we already discussed?

The more improbable claims that don't logically imply each other they make, the higher the chance that they are lying.

The longer they talk, the more unlikely it is a priori that what they're saying is true, but the greater evidence you have (since they're less likely to make that exact claim). I'd say the stuff in the Book of Mormon is the sort of thing that is more likely for someone to say than for it to be true, so each statement makes it less likely, but if you believe the Bible, you clearly don't think that.

Wikipedia makes many improbable claims that don't logically imply each other. I'd say that, a priori, it's far more likely for the Book of Mormon to be true than Wikipedia to even be mostly true. But since it's also a priori far less likely for the more detailed Wikipedia to exist, I would be willing to bet at good odds that Wikipedia is almost all true.