Not the best way to do it. The Russians replaced the unstable tritium with nice stable lithium deuteride. I forget the exact mechanism, but I think the neutron flux and pressure of the fission explosion causes the Li of the LiD to convert to tritium, which then fuses per normal, yielding a bigger bang and a more stable warhead.
Boosting fission bombs, particularly where the pit is often removed may be a different matter. Not being a physicist, I could not say if you easily figure out the mechanics of stuffing solid Lithium Deuturide fuel capsule into a metallic Plutonium pit during manufacturing, or how well it would work.
Tritium being a gas, is easy to store by itself. Does not have a long shelf life, so needs to be renewed periodically. One of the problems being run into with our stockpile.
Since it can be injected quite easily into a hollow Pu pit, I gather that this is one of those "if it ain't broke, don't fix it" designs that has evolved in nukes.
If wrong, would love to read more, have read about this for longer than most Freepers have been alive. Sick fascination, perhaps, but I grew up with the duck and cover crap in schools.