Q: I've lost my iPhone and have managed to sync my photos into iPhoto via iCloud. Do I need to backup my photos so they don't disappear? And if so, how do I do this?

Yes, you should backup the photos that you have in iCloud.

have managed to sync my photos into iPhoto via iCloud.

iPhoto does not support iCloud Photo Library.  Are you using the new Photos for Mac application?

What are your Preferences for iCloud in Photos > Preferences > iCloud? 

• If you enabled "Photos > Preferences > iCloud> Download Originals to this Mac", as is the default, You have copies of all iCloud photos on your Mac, and your backup of the mac will backup your photos as well, for example your Time Mchine backup.
• But if "Photos > Preferences > iCloud> Download Originals to this Mac" is not enabled, you will have only optimized versions on your mac. In that case open the Photos.app on your iCloud webpage at www.icloud.com and download all photos directly to a folder on a backup drive.

Archive or make copies of your iCloud data - Apple Support