That should be fine. We just did this, I think we came into Frankfurt around 7:30AM and were on the 10:45 flight to Dubrovnik. In spite of its size, Frankfurt Airport is pretty easy to navigate, especially as you will stay in the the "Lufthansa" half, Terminal 1. You should have time for a leisurely meal with many choices. If your incoming flight is really delayed, expect help from the staff for your connection, they are very efficient there (we made a 10 minute connection there once because of our late arrival). Because Croatia is not in Schengen, you will be taking a non-immigration path, the only checkpoint is you may have to go through security screening again. I believe there is a way to miss this via a tunnel to stay airside when arriving A concourse and departing B concourse, but we keep failing to find this route.