I never really understood "Healing assignments" in a raid. More so in 10 man. I feel it is the responsibility of any and all healers in the raid to keep everyone alive and react to any situation.
In 10 man, you have 2-3 healers. CD's can be easily coordinated in your speech program, and if anything unexpected happens, I would expect all healers to react to it as quick as they can to keep the raid/tank alive.
In 25 man (Which I raid in normally) you can have 5-6 healers. Here it makes a bit more sense to assign 1 or 2 "tank healers" and the rest to the raid, but honestly, tanks are taking high damage at a scripted time and duration. You can have one person "watch over them", and they can focus on them more during those times, but honestly any good healer would be already healing them just as much if the rest of the raid is stable.
Over-all as a healer, if you are intentionally not healing specific players because it is "Not your job" or "you were not assigned to it" then IMO you fail as a healer and should learn to adapt more to keep the whole raid alive. If you are ONLY healing a specific target/tank for the whole fight because "it is your assignment" they you are also doing it wrong and should tunnel vision less.
Sorry to the OP for this mini-rant, I'm not saying you are doing any of these things specifically, but to me, healing assignments should be understood by having a synergy with your other healers and knowing how they heal and what they do. All healers should be "raid healing" to a point and only defer to specific targets if EVERYONE in the raid is taking random spiky damage that cannot be caught up with just normal AoE healing.
Lastly, back to specific resto druid info: Yes, Keep LB on a tank at all times, refresh it with nourish for the most part and if you see him taking more damage and the raid is well off, don't be afraid to throw in one or 2 healing touches to help stabilize him.