Very interesting to see your opinion of this excellent camera. I bought the Panasonic version of it (the L1) when it was introduced in 2007. I used it regularly until I sold it in 2012, and sometimes wish I hadn't.
I don't know your focal length preferences, but can highly recommend these two, very different, native 4/3rds lenses.
The Pana/Leica 25mm (50mm equivalent) - a bit on the large side but has an aperture ring and produces wonderful 'Leica like' images.
The Olympus Zuiko Digital 35mm 1:3.5 macro. 70mm (35mm equivalent), cheap, but small and pin sharp, specially for macro close up use.
I hope you have as much pleasure out of the Digilux 3 as I had from my L1.
All the best