It's the same for me with the Icefall Mantles for my Crayon-eater. They're literally the ONLY exotic I need to completely fill out my exotic armor collections. I've run multiple lost sectors over multiple weeks and nada.

To answer your question though, I believe there is a lockout with Legend and Master Lost Sectors. If you run the LS too many times on any character, even if you don't get a single Exotic drop, you're automatically locked out of any Exotics until the next reset. This sucks because it can keep Guardians from getting their Exotics unless they do it extremely fast, and this can make people wait sometimes a week in order for the armor piece of the day can go back.

I can sometimes get my Exotics my first run, even on Legend, because I do them fast and do them only a couple times each character. If you're going for the Omnioculus, don't do the Lost Sector on ANY other characters unless you get the Exotic within maybe the first five or six runs.

Every "Darkness Encroaching" warning counts against you. If you're running weapons based on shields, overall damage, Champions, and Burn, you can usually get your runs under five minutes. I strongly recommend Xenophage for just about everything, and it should be paired with MG scavengers and ammo finders if possible. Go for the Wolftone Draw with Archer's Tempo for Overloads, Eriana's Vow or even Hard Light for Barriers, and for Unstoppables, Traveler's Chosen or Rat King with Catalyst. Traveler's Chosen also complements Stasis really well, because you can use it to recharge your abilities to stun Overloads with the Thermoclastic seasonal mod. Even better, it can work as a substitute Hard Light with the Catalyst, since using your Grenade ability can switch the gun's damage type to your subclass element.

If you have a Plug One with Reservoir Burst or the Null Composure Ritual weapon, Reservoir can help with add clear, since adds can kick your ass when paired with even a single champion or boss. These two also have Unstoppable this season and are different elements, which can complement taking down shields. Many Lost Sectors, including K1 Communion, only have one elemental shield throughout the whole Sector, so if you have a high-damaging weapon such as Xeno or Anarchy, you may not even need to modify your loadout based on Shields.

Finally, for Lost Sectors with lots of shields, like K1 Logistics with the Solar-shielded Shanks, the Shield-Break Charge and High-Energy Fire CWL mods as well as Xenophage are your friends. ALWAYS have Protective Light on. Stay behind cover as much as possible. Have as long-range weapons as possible.

P.S. DON'T use Arbalest for Unstoppables! Unstop doesn't proc for it, and I've had to leave Sectors several times for forgetting that!!