Originally Texas wanted a Big 12 network much like the SEC network, but couldn't get the other schools to go along. Then they tried to partner with OU on a network, but OU refused. So they did the LHN on their own. It wasn't easy to start a network. But there were no legal or contractual barriers. If Texas joins the SEC, certainly a part of that will be contractual provisions giving the SEC network all of that content. So I don't think restarting the LHN network, if it goes away, is at any risk of returning.
As for pushing around other schools, that might work with SC or Mississippi State, but schools like LSU, Florida, Georgia are large confident institutions that won't buckle the way TCU, Texas Tech, Kansas State, Iowa State and the like will. Texas was Andre the Giant among a bunch of midgets in the Big 12. In the SEC there are too many Hulk Hogans and other large creatures for even an Andre the Giant to rule the roost. In the Big 12, Texas dominated because their were half a dozen schools that said "whatever Texas wants" on any decision. I don't think those will exist in the SEC.