Whenb you're at CAI watch the live flight info like a hawk. You should know which flight is coming in that you will board so you can work out if it will be late as many airports don't show a flight as delayed until it has docked at the gate. If there's the slightest sign that you will be delayed call LH and tell them that the reps in CAI were no help and ask to be booked on the direct CAI-MUC flight. I'm sure people will flame me for this but it has worked multiple times when I've had FRA-MUC double connections.

Your second job ahead of flying is to be aware of alternative routes with *A carriers. If you miss either connection go to the LH service desk and tell them which flight you'd like to be on, but be flexible. At this stage ask the rep if they have any info on EC261 rights. This will "encourage" them to get you to your destination within a reasonable time of your original arrival (NB: Don't threaten them! Just ask for the info.)