Lindsey is seems to be making two arguments: one about political strategy and one about ideological affinity. These arguments overlap a bit, but I think they ought to be handled separately. I'll put it as a Q and A:
Will libertarians achieve more if we disassociate ourselves from the right?
I've never felt a particular affinity for the right. But Lindsey is probably addressing politically active/ influential libertarians, of which I am neither. I imagine he's also trying to push Cato a bit away from it's association with the Republican Party as well.
Anyway, I would answer "Yes", because I don't really see the point in blanket political alliances Lindsey's suggestion that libertarians should make alliances on a case-by-case basis seems obviously right. Associating yourself with a political party for it's own sake is stupid.
Are libertarians more ideologically affiliated with modern American liberals?
Depends on the libertarian and the liberal in question. Many libertarians are basically, to use Will Wilkinson's phrase, "liberals who like markets". But then there are the Randian leave me alone types, who, though I may agree with them on many specific policy issues, don't seem to care a lot about promoting human welfare (that's probably an overstatement).
But both of these put together represent maybe 5% of the American population. There are a lot of Americans with libertarian beliefs, but, in my experience, they have plenty other very non-libertarian beliefs.
I guess where this is leading me is that ideology as a way of categorizing a large group of people is a pretty big abstraction from reality. My feeling is that it would be enough for Lindsey to point out that republicans, and the Tea Partiers, have a lot of beliefs that libertarians probably disagree with. From there, individuals can make up their own minds. Isn't that the libertarian solution?
Not really related to the above, but I see this kind of debate as being largely about identity. A lot of libertarians may feel the need to associate themselves with other, larger movements or subcultures.