You can buy USB external optical drives, or tether one over a network from another machine.
The license (last time I looked, and for the direct download from Adobe) allowed for being installed on up to two different machines at any one time, regardless of operating system, but technically limited to only one being in use at a time. So you can install on your desktop workstation and your field laptop so you can work on stuff at either of them, but you're not supposed to install on your computer and then your buddy's computer so you can both use it at the same time.
And in the case of getting a new laptop you would simply remove one of your installs from the old device you are replacing. As far as I'm aware Lightroom doesn't have any really draconian Digital Rights Management attached to it, and doesn't limit installs even if you are violating the license.
Canon EOS 7D | EF 28 f/1.8 | EF 85 f/1.8 | EF 70-200 f/4L | EF-S 17-55 | Sigma 150-500