Was he working on a dirty bomb?
No idea....lots of theories as to just what was going on.
Could've been a smuggling operation or someone wanted him dead....your guess is as good as anyone's.
If it wasn't a hit (and using a $10 million to $25 million dollar weapon when a bullet fired from a really nice sniper rifle or a $30 dose of ricin would have done the job just as nicely doesn't sound like a hit), a dirty bomb, or worse seems likely:
Polonium-210 mixed with beryllium-9 produces a strong neutron source. Plutonium bombs, including 'suitcase nukes' need a neutron source as part of the trigger mechanism. It's the part that needs to be renewed to keep them in working order.
Given his Chechen connections and conversion to Islam, Litvinenko may well have been supporting a project to revive an old plutonium bomb some Islamist group had acquired.
The multiple contaminated sites, and multiple doses he seems to have received fit as well with Litvinenko carrying a container of Po-210, which, unknown to him had a leak, and managing to ingest some on a few occasions, as with multiple attempts to kill him using a bizarrely expensive means.