If you mean Creative Cloud Lightroom, No. Same as the serial-number-licensed LR, you are limited to 2 computers by one user, and not simultaneously. Cloud licensing enforces that when you try to log into the third computer it’ll deactivate the other two, and then you can reactivate one of them, so you can legitimately install and use CC apps and LR on up to two, but not three.
If you are asking about seamless data synchronization, no to that, as well. You can choose collections of photos to synchronize with the cloud to iOS devices or the lightroom.adobe.com website, but not amongst desktop computers. I use a USB3-WD-Password HD to work on LR between my two licensed computers, where both the LR catalog and photos are on this external HD.
Not sure if you're talking about Lightroom, or Lightroom mobile, but Lightroom is an app which must be installed on each computer where it's used (it's not a "web-app" like netflix or hulu).