I have broken a lower right tooth - 2nd from back tooth. The dentist says that I need crown lengthening to prepare for a crown. Is is better to have a crown or just remove the damaged tooth?

Are you missing any other teeth on that side of your mouth and if you are is it directly above the broken tooth?
Ideally, it is better to restore than remove. When a tooth is removed the teeth on either side and above or below it will move which can cause future problems.

I just had the crown lengthening done about 24 hours ago and was also told it is better to preserve the tooth whenever possible. My tooth was cracked and not enough tooth exposed to hold a crown.

What is a crown lengthening? Hope I don't need that... the endodontist filed the back part or my tooth practically to my gum.

This will give you an idea of what crown lengthening is yogiP.

Crown lengthening - Wikipedia, the free encyclopedia