Squeeze the crabmeat gently to remove any excess liquid, and pick through it to remove any bits of shell or cartilage. Gently mix the crabmeat, mayonnaise, sliced basil, jalapeño, and the remaining 1 tablespoon lime juice in another bowl. Season with salt and pepper to taste. Spoon the crab mixture over the avocado mixture, forming a second even layer and smoothing the top. Cover and refrigerate until ready to serve.