Licensed assisted access is a advanced version of LTE-U technology. In LTE-U, eNodeB treats WiFi as a carrier but it is unlicensed. Because of WiFi as unlicensed space, many co-existence are possible that may result interference. LTE-U solution does not follow the principle of Listen Before Talk (LBT) that is the main reason of interference. In United States, South Korea and India, there is no enforcement of LBT over the unlicensed spectrum. It means, LTE-U can be deployed in geographies where LBT is not mandatory.
But in the other part of world specially in Europe and Japan, regulatory bodies enforce to use LBT before using unlicensed spectrum. For that, LBT is implemented in LTE-U and it became LAA.
As per my understanding, LAA uses carrier aggregation principle but not exactly the same as LTE-Advanced CA feature. Here there would be need to change software and hardware at eNodeB and UE both.
Initially, LTE advanced carrier aggregation feature emphasized on aggregating licensed carrier. But later, the same principle is used to derive many options/variants of carrier aggregation feature.