With my basic understanding of German and Google translate, I come to the following conclusion: yes, this keyboard will function basically if not completely with LMMS.
On the site, you can see that the keyboard contains its own USB-MIDI interface, and assuming you're using ALSA, you'll be able to plug-and-play out of the box forwarding notes to and from the keyboard.
Bonus functions like the tap tempo buttons may not function at first, but assuming it's a standard, it shouldn't take much Googling to make it work like it should under Ubuntu or other Linux Distro.
The software provided of course likely will not work, but should be emulate-able using WINE.
Yes, this keyboard will work with LMMS.