Any form of power generation could be used in space. It's a question of whether it's financially and practically feasible. From a spacecraft perspective mass is a huge contributor to cost - typical estimates are $10,000/kg.
Now from what I've read on Wikipedia about LFTR, they can produce a whole lot of power in this table it seems the most efficient system produces 1000-MW(e) from 700kg of fuel. That lasts approximately 12.5 years according to the reference. Lets assume that that time span is acceptable for our mission. However we probably don't need 1000MW - or anything close to that; depending on the payload you're designing for you power requirements might be tiny or huge but 1GW is larger than I recollect hearing (maybe look into Lunokhod since the rovers are RTG powered).
The question then becomes scale. Can you effectively scale down your 1GW design to 1MW? That might be more in the range that would be useful for spacecraft. You probably can't assume it's simply 1/1000th of the mass since smaller engines typically have larger dry:wet mass ratios. We haven't actually covered dry system mass yet either. I can't find any estimates for the dry system mass (dry mass is total mass less fissile material mass) but typically with anything nuclear related it can be many thousands of time the fissile mass. So a 700kg fissile mass may require a system mass of hundreds of tonnes, or more.
However that all being said, if there is the need for a huge, high power spacecraft like those seen in sci-fi films it may be a reasonable alternative to solar power especially for interstellar travel - at pluto you're spacecraft would require truly gigantic solar arrays to match power with this system.