Mach 6 buys you roughly 1.8 km/s at those altitudes. OK, let's say that X-15 reached 2 km/s for good measure. But at that speed, Newton still works against you and you're not going to perpetually miss the Earth because of carrying so much momentum in the velocity vector that you're effectively free-falling in a circle around it. To achieve orbital speed you need to go roughly 7.5 km/s (about Mach 25).
But at the altitude that you still gain any aerodynamic lift, and where such a lifting body design still comes useful, your orbit is also going to decay rather fast, and need I say your airframe is probably melting by now if you're still in denser, lower atmosphere below the Kármán line (100 km or 62 mi). So you also have to climb fast and then circularize, at which point aerodynamics don't do anything for it any more, but relatively large aerodynamic surfaces of your lifting body will increase the surface area exposed to atmospheric heating on reentry that you need to somehow protect with a heat shield, if you want to also return from orbit.
That's how these experimental airplanes helped the development of Space Shuttle Orbiter (SSO) - the reusable, lifting body part of the Space Transportation System (STS). They helped establish limitations of then on the cusp materials science and propulsion technologies, dynamic pressure on the body at rapid acceleration through lower atmosphere, and so on, and some of those findings were used to design the SSO while also helped dismiss failed, infeasible ideas so it ended up being relatively safe and reliable.