RADEONGRAPHICS211

You cannot use the links as they are not for Note 3. The process however is identical to the one you need to do for Note 3. Go to LineageOS web page. Find your variant of Note 3 (there are at least 3 variants and you need the correct one). There is an instruction page there. You will see that the process is the same. I highly recommend doing that for Note 3. I did it a few years back and it gave a few years more life to the phone.

How do you measure your ping?
 
Ping is actually latency and it's always against some destination server. Latency is increased by any active device between your NIC and the destination server, and thus the issue could well be in any of them. You can get a latency value for any layer 3 device between your NIC and the destination server by running a traceroute. I say "a value" because they're not always accurate since ICMP responses are not a priority to network devices.
 
So, back to it. How do you measure your ping?