1) Delete any flat out bad shots on import (or skip importing them). Ditto for any video you've taken but don't need anymore (dunno about you, but I snap random videos with my DSLR now and then, but only once was it for actual use outside "I want to show this to someone later", and they take up way too much space to keep).
2) Rate photos. When you need space (assuming you didn't do it when you rated them) you can always wipe out the ones you'll never use.
3) Check for duplicates and redundant near-duplicate photos. Delete those, too.
Teekesselchen: Home is a lightroom plugin to help find and flag duplicates. It works pretty well. You have to watch out for action sequences when you shot more than 1 photo per second, but it's not too bad about catching those
That will reduce the sheer mass of photos.
Then,
4) Use smart previews in Lightroom so it doesn't *look* like anything's missing when you're offline
5) Put all your photos you aren't likely to need soon on a network drive in your home (I archive by quarter now, sort of. I have everything from January 1st til now on my laptop and the rest is on a network drive. Sometime between May and July I'll probably push January through March off to the network drive.). That way you only have to carry around a small subset of the images, but with smart previews, lightroom will still let you do edits to them as if they're there, and you can even export them in web-quality sizes.
Beyond that, you should be backing up to the cloud. There are lots of options there, both photo specific and for all your files.
Don't use carbonite, though. Unless they've changed their policies, it will take almost a year to back up your photos (last I looked, they restrict upload speed to about 1 GB per day)
This looks like a decent overview of available options.
Backing Up Photos to the Cloud / 2014
it doesn't mention amazon prime photo, which might have come out after the article was written - that offers free photo storage to Prime customers. The interface is terrible, though.
https://www.amazon.com/clouddrive/primephotos