No, since the Lisa mouse could have come from a Lisa 1.
Whether it has a hard drive or not depends on whether it's a Lisa 2/10 or a Lisa 2. (The 2 or the 2/5 are the same Lisa, the only difference being that the 2/5 shipped with an external Profile hard drive.) The Widget drive looks like this:
http://john.ccac.rwth-aachen.de:8000/patrick/data/Analyzing_2004.jpg
(it's the one right above the floppy drive - to the left is what the inside of a Profile external hard drive looks like.)
If you have a 2/10, you'lll have an internal hard drive, which you can tell by opening up the front case and looking above the floppy drive. It will also not have a parallel port on the back of the Lisa since it's internal and routes to the widget drive.
This is what a 2/5 looks like with the Profile on top of the Lisa: http://www.obsoletecomputermuseum.org/lisa/profile.jpg
There should be a 25 pin cable hooked up between the Lisa's parallel port and the Profile drive.
Note that it's not a good idea to place the profile on top of a Lisa as in this picture as the Lisa's top isn't flat, so you'd be endangering the hard drive. Keep in mind, if you have one of these, that they're very old and very fragile, so you should do anything you can to preserve them. (Not you personally, but in general.)
Whether it has a hard drive or not depends on whether it's a Lisa 2/10 or a Lisa 2. (The 2 or the 2/5 are the same Lisa, the only difference being that the 2/5 shipped with an external Profile hard drive.) The Widget drive looks like this:
http://john.ccac.rwth-aachen.de:8000/patrick/data/Analyzing_2004.jpg
(it's the one right above the floppy drive - to the left is what the inside of a Profile external hard drive looks like.)
If you have a 2/10, you'lll have an internal hard drive, which you can tell by opening up the front case and looking above the floppy drive. It will also not have a parallel port on the back of the Lisa since it's internal and routes to the widget drive.
This is what a 2/5 looks like with the Profile on top of the Lisa: http://www.obsoletecomputermuseum.org/lisa/profile.jpg
There should be a 25 pin cable hooked up between the Lisa's parallel port and the Profile drive.
Note that it's not a good idea to place the profile on top of a Lisa as in this picture as the Lisa's top isn't flat, so you'd be endangering the hard drive. Keep in mind, if you have one of these, that they're very old and very fragile, so you should do anything you can to preserve them. (Not you personally, but in general.)