The Creative Cloud Photography plan comes with 2 GB of online storage that can be used for file sharing:
The free Dropbox account also provides 2 GB of storage for file sharing, which can be increased up to 16 GB by referrals:
Assuming that you are working with raw images, you want to export high res jpeg or tiff files to send to your client. High res can mean a lot of different things. Find out how large they really need first. With both dropbox and the Creative Cloud plan, you can instal the a desktop app which creates a folder on your hard drive, then you can export from LR directly into the folder. This saves the pain of having to upload anything through a browser.