Jun 12, 2016 - 6:20 AM
I don't think you can make it back to Lucerne before 11 AM, but you can check the timetable. I would not do it if the peaks are in the clouds, but actually it does not look that bad this morning. Perhaps you can take a boat or bus to Vitznau, take the train to Rigi Kulm, then the train down to Arth-Goldau and proceed from there to wherever to wanted to go today.
A boat trip should be doable. Again, check the timetable (link here) or walk over to the boat dock to ask about your options. One option might be a boat to Alpnachstad and back to Lucerne. Or the boat to Küssnacht am Rigi, then walk 400 m to the train station and take a train.
I hope it works out, have a good day!