The Louisiana Purchase was an enormous expansion of the territory of the United States. It was ironic that Jefferson, a man who believed in limited government, took the action of acquiring this land from France. There are two possible answers to your question regarding liberty.
First, we can, as with the results of the Mexican war forty-five years later, conclude that "liberty" was favored by the acquisition of territory for the U.S., given our democratic system of government--which did not exist in France and French territories at that time. Obviously, the larger the U.S., the more people eventually would have the opportunity to live under a democratic government.
The second possible answer, however, is a negative one. Unfortunately and tragically, much of the Louisiana territory was added to the U.S. as slave states. It is even possible that this was Jefferson's intention. And obviously, the Native Americans were adversely affected by the huge westward wave of settlers who eventually populated this territory.
Throughout his entire career, Jefferson spoke and wrote against slavery, but remained a practitioner of it. His entire persona was one of self-contradiction, not only with regard to the slavery issue but the general concept of liberty. During the French Revolution he resisted accepting that the movement had deteriorated into a tyranny, despite the reports coming to him from his envoy in Paris, William Short. As Secretary of State, Jefferson was part of Washington's first-term administration, but took steps to undermine Washington's policies. Jefferson's heritage for the U.S. is a mixed one. On the positive side, he was the principal author of the Declaration of Independence and, along with others, in the creation of the Virginia state government he spearheaded the elements that eventually were central to the Constitution of the U.S. But on the issues of race and slavery, he was not in the forefront of enlightened thought, to say the least, and these contradictions are relevant to our evaluation of Jefferson's enlargement of U.S. territory. Additionally, though Jefferson expressed sympathy for the indigenous Americans, his policies as President did nothing to prevent the encroachment of their land by settlers, which was accelerated by the acquisition of the Louisiana Territory.