Yes, I'm sure it will work really well for your application
The Lithium doesn't make a lot of difference - in your case you are actually reducing the bike's load (i.e. the supplied current to the bike), so the Regulator will actually shunt a bit more than it would with std incandescents. But that unit should still be just fine.
If you can find one, get the 06-07 Honda 1000 one essentially same device as the 600, but it only has a single plus and minus output vs the 600's which have 2 of each - much easier to integrate the 1000
Of course you need to install the appropriate connectors
(Just be careful of knock-offs)
Here's a few in US in decent shape at decent prices
If you want to buy new - I haven't personally used Rick's HotShot Regulators but they seem to get good reviews - certainly their customer service is fabulous and their stators are the best after-market available. On the subject of Customer Service, if you ask, I bet they would put whatever connector(s) you want on there for you.
That part would appear to be a 10-159 for the Honda - their specified replacement for the Triumph is actually a different model.
(Obviously the Honda is a already an OEM MOSFET, while the Triumph is replacing an OEM SCR module, so not a direct 'type' replacement)
You can ask them how their specs compare.