Adding a third computer

In general that’s not possible. You can, however, install the software and when you need to use the third computer, disable the license on one of the 2 other computers. This is the only possibility to run Photoshop on more than 2 computers.

In addition, when not licensed, you still can use Lightroom to browse your pictures and export them, but you will not be able to edit.

A last possibility is to use Lightroom mobile for your synced collections. That’s also great to edit your pictures with an iPad or similar, when you are on the road. The only problem with that is, that only one catalog can be shared and the pictures need to be in a collection that is synched to the cloud. In that case you’re working on proxy images (good enough for web exports).