I think this is a case of a word having one colloquial meaning and a different technical meaning. If you "lift" something, you're probably picking it up.
In a hydrodynamic sense, "lift" is a force on a foil moving through a fluid. This kind of lift is a force orthogonal to the direction of motion through the fluid and the surface of the foil. That could be upward lift, like that on the wings of an aircraft. That could also be the forward and leeward lift on the sail of a sailboat, or the windward lift on the sailboat's keel. It could also be the lateral, stabilizing lift on the control surfaces of a rocket.
Maybe hydrodynamic lift is what was meant, but if so, it wasn't well described; it sticks out in memory precisely because he made it sound like the fins contributed on net to reaching orbital energy and I might've yelled at the screen a little bit about that.
In a hydrodynamic sense, "lift" is a force on a foil moving through a fluid. This kind of lift is a force orthogonal to the direction of motion through the fluid and the surface of the foil. That could be upward lift, like that on the wings of an aircraft. That could also be the forward and leeward lift on the sail of a sailboat, or the windward lift on the sailboat's keel. It could also be the lateral, stabilizing lift on the control surfaces of a rocket.