Hello All
I am looking to understand if this trail running route is possible?

https://www.wikiloc.com/trail-running-trails/eastern-troodos-and-quarry-168985827
https://www.alltrails.com/explore/map/checkout-route-255ea88

I understand that most of the route is there but there is a part of the lake B to A, that i am not sure about. Is there a way? Are there any restrictions?

yes, you can pass this route without problems
https://www.strava.com/activities/10201270257