This is a really weird fix/tweak, but it's working for Samsung Galaxy S4 phones running CyanogenMod v12.1(ie. Lollipop, latest nightly), and Samsung Galaxy Tab 2 tablets running Samsung's Jelly Bean v4.2.2 . The faster web browser speed response is immediately noticable :

1. Disable mobile data on phones (to be sure we're just testing Wi-Fi).
    

2. Disable IPv6 on your router/gateway. Fyi, I'm using a Cisco E4200 router/switch/gateway (don't forget to hit Save button to retain change).
    

3. Try an internet search or site :
   Speed Joy! Slow Wi-Fi lag problem goes away in all apps.
    

4. Re-enable IPv6 on your router/gateway (don't forget to hit Save button to retain change). Try internet search :
   Speed Joy! Slow Wi-Fi lag problem still gone away in all apps.
    

5. Re-enable mobile data on the S4's. Full reboot the S4's. Try internet search :
   Speed Joy! Slow Wi-Fi lag problem still gone away in all apps.
    

6. Power off the phones, remove the battery and reinstall battery (to see if the fix/tweak survives a full power-down. Try internet search:
   Speed Joy! Slow Wi-Fi lag problem still gone away in all apps.

Unfortunately, I haven't been able to see what happens when connecting to a different router yet (I'll test that and update this doc later). Apparently, there was something ala IPv6 that the phones (or the router/switch?) were remembering and that was erased/deleted/modified the first time that IPv6 was disabled and then re-enabled on the router. A DNS cache update? I'm not exactly sure, but I'm sure happy that it works :-)