Just as the other poster said, skip the preacher curls. There are other movements that you can perform that are better and will put less stress on the bicep tendon.
My first recommendation is "incline curls."
As far as your biceps failing before your lats, that's pretty common.
You might be doing what many others do when performing lat work you are squeezing the bar so hard that you are activating the bicep muscles.
One more tip: Think of your hands as mere hooks. use a thumbless grip and focus your attention on the stretch that you should be feeling in lats when you work them.