If I borrow a Battlefield 4 disc copy and then buy a different disc copy, will I have to re-install it, using even more PS4 space

You will need to reinstall the game, or update the registry key to show that you have the expansion installed.

http://www.reddit.com/r/battlefield_4/comments/1tbt2p/solution_for_missing_china_rising_expansion_error/

Back up your registry

Log out and fully exit Origin

Open your Registry Editor - Type in regedit in the Search Menu and press Enter

Navigate to HKEY_LOCAL_MACHINE > SOFTWARE > Wow6432Node > EA Games > Battlefield 4

Check for a folder named Xpack1 under the Battlefield 4 folder

If it exists -> Click on Xpack1, on the right pane see if there is a string named

Installed. Double click on Installed string and set the Value data to True

If it does not exists -> Right-click on Battlefield 4 select New then select Key a new folder will be created, name it Xpack1 right-click on Xpack1 > New > String Value > name this string Installed on the right-pane, double-click on Installed, set Value Data to True

5 . Exit Registry Editor

Once all these steps have been completed, log in to Origin and start up Battlefield 4 and join China Rising Maps

I got this help from EA online assist.

One of the possibilities is that one or more of the players in your lobby has a very high PING, which is causing the lag. Otherwise, it could be your own PING. This could be caused by another family member in your house using the internet to download things, watch Netflix, or stream videos, which can really slow the internet down, because it eats at your bandwidth. By ensuring nobody else is doing these while you're playing, it should reduce PING and stop the lag.

Other than that, you could switch from a wireless connection to a wired connection, which usually strengthens the connection. You could also close any background running apps.

Also, try and play in servers close to your location. Playing in servers far from your location can cause lag in the game and reduce performance.

I would reset the internet and keep it off for a while before turning back on, giving it some time to refresh.