Leafs do lack an elite 'shutdown' defensive pair, although they did have excellent results from the Muzzin-Holl pair for a decent stretch while they were really rolling; they've been far from it since though.
I don't think they necessarily need a single 'elite' shutdown pair to go on a run though, or one that has 'shutdown' as it's primary focus. Rielly's defensive game has taken a jump since his contract extension & he was strong in the playoffs too. Chychrun is a solid all-round defenseman (with the tools to be elite) but obviously isn't your primary 'shutdown D' unless he's on a brutal team. Between say Rielly-Brodie & Muzzin-Chychrun though, I think they'd very effectively contain the oppositions top lines & close out games. Because of Rielly's improvement, Rielly-Brodie + Muzzin-Holl (with Chychrun reducing their workload some) could be good too if Muzzin & Holl can get closer to what they were.
Even Liljegren has shown a lot of potential & flashes of shutting down the opposition (especially his aggressive gap control to disrupt play & how efficient he is retrieving & breaking out), but he should stay sheltered this season; he's shakey at times & isn't the strongest around the crease or in battles.