The Targaryens control fire breathing dragons and are not harmed by fire. The Lord of Light is a fire god and fire is used in worship/magic by it's followers.
The Targaryens came from Valyria, where the LoL cult is quite common.
Are the two related somehow?
No, there's no significant connection between them. In fact, the Targaryen's didn't even worship R'hllor at all.
In the show we haven't heard very much about Valyria in it's prime (yet), but I was unable to find any evidence that R'hllor worship was common in Valyria before it exploded. Valyria instead had it's own religion, where the people worshiped a Pantheon of gods. In the novels, we are told that the Targaryen's named their dragons after these Old Gods, e.g. Balerion, Meraxes, Vhagar and Syrax. Otherwise, though, the Targaryen's were mostly non-religious, but adopted most of the customs of the Faith of the Seven when they conquered Westeros.
The fact that both are strongly connected to fire appears to be simply the nature of fire as a primal force, so it's a recurring motif with different meanings in different situations.
