The best way would be to store your Lightroom Catalog and the original images on an external drive and plugin the external drive on the machine on which you want to start editing.
Adding to Chetna's answer ... Lightroom cannot have photos stored in the cloud. All photos must be on an internal or external or network drive.
Will not work with Google Drive but will work with Western Digital's My Cloud ?
( My Cloud is a private personal storage unit that plugs into your home network.)