Yes, there are alligators on Cross Lake. There are alligators in nearly all large bodies of water in North Louisiana. However, interactions with humans are pretty rare. If you live directly on the water and have small pets that roam the shores there is always a possibility of issues, albeit a small one. Nothing that a fence cannot solve though. You should love Shreveport Louisiana. There are many lakes, rivers, etc in the area to enjoy.
It is against the law to hunt / fish alligators on Cross Lake without a tag. This alligator was taken from Hideaway Harbor neighborhood private lake which connects to Cross Lake in 2009. The alligator was taken with a tag.
Cross Lake Shreveport 
Is it safe to swim,and have there ever been any reported attacks on humans?We Recently moved cross lake,Cottons pocket,And were asked if it was safe to swim we had no reply,Because we were unsure.
you will be ok to swim im 15 years old and have swam in that lake for years never had a alligator attack me but I have seen tons of gators in the lake but interactions with. A human are very rare