Absolutely that is correct. BUT, what we have fail to understand in this concept of loyality to his state is, that it also meant loyality to a constitutional republic form of national government. The Constitution was based upon the States being the governing power, not a centralized federal Government which exercised power over the states. Lincoln was changing that system of Government and the "Republicans" had so stated that was their intentions to do so. That this new Government would exercise powers that they did not have over the states to end slavery. Much like our present day medical care debate and illgal immigration issues. Slavery under that Constitution was a STATE issue and was made a federal issue by the abolishionist and Republicans trying to exercise their desires over those states and their sovergnity rights.
You see the Constitution only gave the Federal Government to right to act against the states only in the case of its own self defence. Such as in the case of rebellion which would be the attempted overthrow of that government by force. The Southern states secession did not threaten the overthrow of the US Government, and did not meet that standard in which the government could use force and act against the states, but Lincoln said it did. That is why the Lincolnites had to trick the Southerners into "firing the First shot", (I.E. Fort Sumter).
We have lived under the form of Government we now have for so long that we do not really understand this concept of a Republic form of Government. That is where I feel that we make our mistake in evaluating men like Lee or Johnson, or Beauregard, or Cooper, is that we do not understand the times that THEY lived in. We interpose our own understanding of how government is acting now to their thinking.
Lee, for nothing else, seemed to be a Constitutionalist who was devoted to his country over, as you said, the detriment of his own interests, and dare I say his family. So why would he change his mind and choose his state (read in here family) over the very thing he had chosen all his life? There has to be a common ground between the two ideals for Lee to be consistant in his life choices. I am sure that as Lee wrote his daughter it was a hard decision to make, and not for the reasons that we would commonly think. I believe that it was deeper than that because he had no problem in making those same decisions earlier in his life when it was the army, or his family. But War coming to your doorstep is something else, isn't it?