Lithium blankets are still very much in the research stage. The US gets its tritium for it's nuclear arsenal by irradiating special rods called tritium producing burnable absorber rods (TPBARs) containing lithium-6 in a nuclear reactor, specifically Watts Bar Reactors 1 and 2 at the TVA. Each TPBAR is about ten feet long and less than half an inch in diameter. Over about 500 days of burning, each produces about 1.2 grams of tritium.

Civilian sources are primarily from CANDU reactors, but building more of these can be problematic as they're heavy-water reactors (they produce tritium by deuterium neutron capture) and are considered to be proliferation risks, raising both political and legal problems. They also don't produce that much. According tothis paper on sourcing tritium for fusion use, the CANDU 6 reactor, a 700 MW design, can generate only 130 grams of tritium per year, though not all of this can be captured.

According to ITER's own numbers, 800 MW of fusion-generated electricity will require 300 grams of tritium per day. Lithium blankets are the most promising way to get this done, but they present their own technical challenges. This is why research is happening on other approaches like laser confinement and Z-pinch to find ways of using just deuterium.