Tritium is in thermonuclear weapons, suitcase nukes are (to the best of my knowledge) solely fission weapons Tritium is used in tactical nukes. Tritium is a strong emitter of alpha particles. If you have alpha particles hitting beryllium nuclei, the beryllium transforms into carbon, and emits a neutron. The neutrons can then trigger fission.
I'm guessing that if you had a core of tritium, surrounded by beryllium, surrounded by plutonium, and you used explosives to suddenly compress the mass to absurd densities, you would have enough neutron flux to set off the plutonium.
Then again, I'm an engineer rather than a professional physicist, so I may be totally out to lunch
Tritium is a Hydrogen isotope. There are 2 neutrons and one proton in it. An Alpha particle is a Helium nucleus and contains 2 protons and 2 neutrons. If you're to have Tritium acting as an alpha emitter there's going to be Fusion going on and by then we're way past suitcase.
The case nuke merely needs a subcritical mass of plutonium to be compressed to criticality. Enhancements to reduce material quantity involve a good reflector (beryllium) which will reemit\redirect errant neutrons from the fissile mass back into the mass.