I think it depends on the lens, and how you plan to use it on both DX and FX in the future, as well as how imminent your move to FX is.
If FX is just a farflung dream, and you're hoping to get there someday, then FX is probably not a great purchase for you. The lenses are bigger, heavier, more expensive, and not always suited for DX use. If, however, you plan to move to FX within a few months, and DX is merely a temporary stopgap, then minimizing DX lens purchases may make sense.
The main issue however, is how crop factor works. What is ultrawide on FX is merely walkaround on DX. What is telephoto on FX is supertelephoto on DX. Whatever the lens, once you switch formats, the FoV and basic usage of that lens will change on the other format.
If you are using a set of portrait primes, this may not be an issue. 50 on DX is like 85 on FX; 85 on DX is like 135 on FX, etc. Your lenses may be able to cover for each other on FX. But if you rely on a supertelephoto zoom for sports or wildlife, prepare to take a bit of a hit on "reach" when you go FX. For example, the 80-400 on FX has the same angle of view/equivalency as a 53-267mm on DX does. In other words, prepare to do the crop math backwards and watch all your lenses get 1.5x shorter on FX than on DX.
And the sole exception to lenses you should get on DX while you're shooting DX would undoubtedly be ultrawide zooms. Because the lenses that cover an FX sensor that would still be considered ultrawide on DX are rare and expensive, and a 10-20 would probably serve you far better (and much more cheaply) until the move, when you can sell it to fund part of an FX ultrawide zoom lens.