He tends to shine pretty well in the Cove, Courtyard, Farmstead, 3 out of 4 Darkest Dungeon quests, and a solid chunk of the game's boss fights. His high damage to the frontline works well in those places, as the Frontline can be just as dangerous as the backline a lot of the time, meanwhile his high self sustain and being practically unkillable helps a ton in those longer and more dangerous quests.
He's got two amazing self buffs with Withstand and Revenge, adding to his use in any longer battles, boss fights, or Endless mode. His Intimidate offers some nice team support by reducing damage from any heavy hitters(though Intimidate sees little use out of very specific encounters). He has a nice camping skill in Quarantine to stress heal the party at the cost of some of his health(which he can immediately heal up with a single use of Solemnity). And his Purge is situationally useful to clear up Corpses, which coupled with his low speed means he'll get to use it when there actually are corpses laying around.
Outside of the few locations he shines in, he's still a viable character, and more than capable of getting you through whatever dungeon you're heading through, but there are better choices depending on what you're going up against, and a few boss encounters where you wouldn't want to risk bringing him in most cases.
If you're building a party with him, you want to bring anyone capable of Stunning and Damaging the backline, while avoiding characters who do nothing to cover his weakness like the Vestal(Leper doesn't need nearly as much healing as she offers, and since the Vestal offers little other than healing aside from a mediocre stun and poor damage projection, you'd want to bring someone else as a healer who would contribute more).
A Plague Doctor offers great Stunning to backliners, Crusader with Holy Lance or Arbalest with Sniper Shot can take care of backliners, Occultist with Abyssal Artillery can also handle backliners in the Cove somewhat decently. A Jester can buff the Leper's Accuracy and Speed which is very helpful, but does leave you missing out on an extra hero to deal with backliners if he's too busy buffing. Man at Arms can buff Accuracy with Command, and in certain boss fights is an excellent partner as his Guard coupled with Leper's Withstand and another hero with Protection buffs lets you cover the entire team in high Protection, but otherwise can be an awkward partner.
While others can work well to cover the Leper's weaknesses, he does very little to cover for other people's weaknesses. The most team support he has is attracting attention with Withstand's Self Mark(a better tactic nowadays than it used to be, but still somewhat unreliable), debuffing Damage with Intimidate(bit situational), or just killing enemy damage dealers quickly to prevent as much damage from getting to your team(great in heavily offense based teams, bad if you build your teams around stalling and recovery).
Two good teams I like running with the Leper would be..
Plague Doctor, Crusader, Crusader, Leper. The Plague Doctor's Blinding Gas keeps backline targets stunned, while the two Crusaders dance back and forth with Holy Lance to kill backliners. While the Crusaders are naturally slow, Plague Doctor's stuns buy them time to get damage out. The Leper focuses on just killing frontliners, as the backline is already pretty well covered. The two Crusaders offer Stress Healing and regular Healing to the team, and since the Leper can handle his own health and stress that helps lighten the load a lot. It's also got pretty strong camping skills to it.
Arbalest, Houndmaster, Abomination, Leper. A bit front-heavy, but a pretty solid self-sustaining team. The Arbalest's Battlefield Bandage buffs Healing Received, which stacks with everyone's self heal skills to keep the team in the clear. Leper and Abomination can stress heal themselves, while the Houndmaster can AoE stress heal the party with Cry Havoc. Arbalest and Houndmaster handle backline targets, while the Abomination stuns, and the Leper attacks the frontline. If you need extra damage, the Abomination can transform, and with both him and a Leper there's very little that can stand up to that much damage output for long. You've also got the Houndmaster's Mark to clear Protection, which can be useful against enemies with High Protection while also giving the Arbalest even more damage output.
The first team relies heavily on the Plague Doctor's stuns to make up for it's slow characters and difficult backline reach, while the second team showcases a team built around self sustaining heroes, letting you build a party without relying on Vestal or Occultist, which works out well enough thanks to everyone's solid self heals.
This has been my very long-winded and tired wall of text. Basically, Leper's a solid character in a couple of locations and a lot of boss fights, but otherwise there's better picks for a team depending on what you're going up against. You can still get by using him anyway even outside those few locations however, just have to put in more work to use him compared to others like the Hellion who you can just slap into just about any party comp.