Sounds sensible. The old town is only a 5 minute walk across the river from the station, and the Lion is at the far side of the old town, 5-10 minutes further. The Lion is a bit "yes, I've seen it" and that's it. The old town is good to walk around, lots of old buildings in narrow streets and all pedestrianised, plus the famous chapel bridge and the town walls around the back of the old town. I hope your hotel is in the old town.
Titlis needs a full day. First you have to get to Engelberg by train, and back at the end. The trip is nice, getting further and further into the mountains, And once you get to the top you do not want to be rushed, plenty to do and see. Engelberg town is also worth an hour when you get back down again.
With 1½ to 2 days I would say Titlis or Pilatus, not both.
Are you coming soon? So far this Spring and Summer we have been having very wet weather, and more rain forecast for next week. This is not how June should be. Going up mountains should not be done if it is cloudy. Check the webcams on http://www.titlis.ch/en first, and be prepared to be flexible.