Another way to find out what to run might be to look in the package's file listing. I'm not sure how to do this from the command list, but it's easy in the Package Manager, just right click on the package and select "Properties", then click on the "Installed Files" tab. There can be a lot of files to go through (and most of them just data files, libraries & documentation), but this can help if you're not sure what was installed.
I tried out lmms and it doesn't add a menu option to the MintMenu, however you can add one yourself by right-clicking the MintMenu and selecting "Edit Menu". Scroll down to "Sound & Video" (or whereever you want to add the item) and select "New Item". The name can be whatever you want, the command should be "lmms" & you can change the icon by clicking on the picture button in the top left of the window. Click ok and you're done - should be a new entry in the menu straight away.
LinuxMint 4.0 - Intel E6600, Asus P5B Deluxe, ATI X1950XTX, 4GB ram, 400GB WD hdd, Phillips 170B LCD