Absolutely.
I think we need to make a distinction between Lee and the political leaders of the Southern states. The political leaders were all about protecting slavery, and for the most part they saw states' rights only as a means to achieve their end. They were altogether willing to trample states' rights in order to achieve that end, if necessary.
Many Southerners (and Northerners too, for that matter), believed firmly in states' rights as something worth protecting in its own right, however. The political leaders of the South deliberately created a situation that put the federal government in opposition to a supposed state right to secede unilaterally. This put Southerners, like Lee, who was opposed to unilateral secession, in a position where they had to join the secessionists if they wanted to protect states' rights.