Actually, this is perfectly normal behavior with pyroar.
You see, pyroar actually have two different social structures. The first is the more familiar pride or coalition, in which one or two males (respectively) live with up to five or six females and their cubs. Because the function of a male pyroar in such a social structure is typically limited to breeding and defending the pride from other pokémon (female pyroar do all the hunting, navigating, and nest-making for the group), only one or two males are ever needed, hence the other social structure, the nomad.
While pyroar of both sexes can be nomadic, the behavior is more commonly seen among male pyroar due to the importance of females to the group (and the aggression female pyroar display to nomadic females—thus limiting a female pyroar’s ability to switch from one structure to another with ease). In fact, most male pyroar experience a period of time on their own—sometimes even the remainder of their lives, if they’re not able to find another pride to join.
Unfortunately, because many male pyroar eventually feel the need to rejoin a pride or coalition, those that fail to do so do adopt the sort of behavior you’re describing, and due to shiny pyroar’s distinctive coloration, this is likely what happened to the one you’re describing. Fortunately, because his behavior is, as you’ve deduced, the result of loneliness, this means it might not be all that difficult to convince him to join your team. Just be sure to make room for him (as although he requires much of the same things as any other feline pokémon, he is an extremely large feline pokémon), and he will no doubt be happy for the company.