I play on a single player world with 2 other local players. There is a gigantic amount of lag when we play. It is very slow and we can sometimes not play. We put all of our settings on low and it still it the same. It still has lag in the current update. When we first start the world there is a minimal amount of lag, as time goes on it gets worse. To reproduce it: 

1. Have a world with 3 local players 
2. play as normal (place, break, craft, trade).  
   OBSERVEDLag will start to happen (blocks will not appear when mining fast, other plays freeze when on is trading or crafting). 
   EXPECTED Lag, a lot of it.