There are editing tasks Lightroom cannot do. So Lightroom is an incomplete solution and you also need Photoshop.
I use both CC and LR, and several other editing applications as well from Phase One, Imagenomic, hdrSoft, Topaz, Nik, OnOne.
Adobe Creative cloud is a subscription service.
Adobe offers a Photoshop Photography Program that includes both Photoshop CC and LR 5 for $9.99 a month.
https://creative.adobe.com/plans/offer/photoshop+lightroom?promoid=KKVFE
Before Adobe went to a subscription business model about 1/3 of all their software being used in the world was pirated software.
Plus Photoshop came in 2 versions, regular Photoshop ($699 retail) and Photoshop Extended ($999 retail), and those versions got updated every 2 years or so.
Those of us that already had Photoshop could upgrade to regular Photoshop for $199. Upgrading the Extended version was $349, and upgrade pricing was offered 3 versions back. So If you owned CS 2, 3, or 4 you qualified for upgrade pricing for CS 5. If we chose we could skip some of the upgrades.
With the cloud, Adobe makes upgrades available as soon as they are ready instead of waiting 2 years to make the upgrades available.
Photoshop/LR installs on our computer so we can use it offline. But if we stop making the monthly subscription payments Adobe doesn't renew the use license and you can no longer use the Photoshop that is installed on your computer.
So it's not really a cloud type service since the software is resident on your computer.
The first 3 versions of Lightroom were $299 with an upgrade price of $99. Because of it's popularity Adobe lowered the price of LR.
Lightroom can be purchased (we don't 'own' the software but get a perpetual use license and the software on a disc) outside the Creative Cloud.