Do neutral wires need to connect?
So you have 6 neutrals: supply, neutral to two lamps, and pigtails from the outlet and 2 switches. 

If your wire-nuts are not certified for 6 wires, you can use a 6” jumper and nut them 3 and 3 (well, 4 and 4 with the jumper).  

Now this will come up if you have two hots coming from the breaker box:  Every neutral has a partner "hot" - that's most obvious in Romex 14/2 where you have a white and a black. These are monogamous partners: hots do not share their neutrals with other hots. The reason is circuit protection.  If a neutral wire breaks, you want the circuit to go dark, you do not want another neutral to be overloaded trying to handle double load.  Neutrals do not have circuit breakers.   So if you have two hots, you must be careful to keep the neutrals paired with the hots everywhere they go, so all the current always returns on the partner neutral.  This is mandatory with GFCI breakers, since they compare current flow on hot vs neutral to detect leakage.  

It is OK to tie grounds together.