As to the impulse comment that Daniel made.
summerizing the part of the ipulse section in english.
The Ambassador class had too much mass for the impulse engines to push, so they included a set of subspace coils to reduce the mass of the vessel, in a mater similar to the warp coils, but not to the point were the impulse engines can push the starship to warp.
Fact section (at lest fact for make belive)
1) Section 6.1 NG:TM second para half way down, ?This necessitated the inclusion of a compact space-time driver coil, similar to those used in warp engine nacelles, that would perform a low-level continuum distortion without driving the vehicle across the warp threshold.?
2) Section 6.2 NG:TM last para second sentence. ?Current impulse engine configurations acheve efficiencies approaching 85% when velocities are limited to .5 c (or twice the speed of full impulse).
3) Last but not least on the impulse question Section 1.1 second page ?Secondary (impulse) propulsion to provide sublight velocities up to and including .92 light speed (c).?
Section 6.2 does talk about why full impulse is at .25 c but it is a speed limit not a limit on how fast the ship can go. So Daniel (Pull out my trusty zippo) I suggest you review the manual yourself.

So based on this, you don't need dilithium specifically. What you need is as follows:

1) A means to create plasma to carry the energy.
2) A means to keep feeding energy to that plasma (so that the energy travels to the applications, and the plasma stays plasmatic).
3) A means to pulse your energy output so that it can properly excite the warp coils.

Well, 1) is easy. You can create plasma in a variety of real-world ways. No need for antimatter, or even for fusion.

And 2) is open to debate. Most probably, some of the applications require humungous amounts of power, so the energy source has to be powerful - fusion might not be efficient enough for warp drive, if you couldn't pack the required mass or volume of fusion reactors aboard a starship. But probably you could, since a few grams of antimatter (probably but not necessarily antideuterium) were enough to run the drive for two seconds in "Peak Performance".

Finally, 3) is crucial. The TM seems to say that antimatter annihilation energy release cannot be pulsed unless it is controlled by dilithium. This makes some sense - you can pulse the energy release by pulsing your antimatter injection, but this may not give you the required fine control. Dilithium might give higher frequencies and more delicate control than the best possible injection valves money can buy.

But 3) is also dependent on 2). Okay, perhaps antimatter energy release cannot be pulsed with sufficient accuracy without dilithium. But can OTHER energy releases? If 2) says that other energy sources are powerful enough for warp drive, then perhaps there are other means of pulsing those energies, means that do not require dilithium (or paralithium, as used by some races - or "lithium", as mentioned in early TOS).

Without further information, we could thus say that TNG TM gives an all-okay for dilithium-less warp drives, although it frowns on dilithium-less antimatter-powered warp drives.

Take a bitch of a lot of power to move that much mass (even a quantum black hole), so when not used for propulsion, the energy available for weapons should be enormous.