I am designing some immutable classes but I have to have some variables like say .Count to have the total count of the instances. But would having a static variable affect multi-threading?
Because methods like Add, Remove, etc have to update the .Count value. Maybe I should make it lazy property?
Yes, whenever you update a shared variable in a multi-threaded environment you will need to just wrap those updates in a lock.
You might want to consider using functions from the Interlocked class, at least in the example you gave.
If you're just doing a counter, interlocked operations may be an option as well instead of a lock. MSDN has a nice example of this in the context of a reference count.
But would having a static variable affect multi-threading?
sure! shared state is affected, by defition, by multi-threading.
Because methods like Add, Remove, etc have to update the .Count value. Maybe I should make it lazy property?
it's better using a class that does an atomic add (like AtomicInteger in java) in order to avoid locks: take a look here