I think you think I was arguing with you.
No worries; I can accommodate.
Let's get the missile out of the atmosphere (by 40km altitude, so still in the stratosphere, we've cleared all but a thousandth of it. The key isn't just thickness but pressure, which is a good read of remaining atmospheric interference.) and then hover. That will require a constant thrust of about 9 m/s² for whatever duration. If the duration is 10 minutes, that's 5.4 km/s impulse peed away on the hover.
It's more efficient to throw the weight over and not just up.
I could also be getting hung on terminology. Lift is generally understood to be aerodynamic, whereas missiles produce thrust. I think/hope I followed your intent though. cn