Which kind of lag are you experiencing? There's two main types. One being where your Minecraft freezes, and your FPS drops. This causes you to "glitch" around. The second type being where your FPS remains intact, and others seem to be glitching around. Another effect of this is delayed commands/chat, and a low connection in tab.
If you experience the first one, it is more than likely due to your PC not being able to handle the server. If this is the case, I suggest optimizing your settings using optifine to as low as you feel necessary to reduce this effect. Another process which can help is allocating more memory to your Minecraft if you have the sufficient memory (RAM) on your PC. If you do not know how to check your RAM, google (or bing) "How do I check my ram (insert operating system)". Simple as that. If you continuously have to restart your Minecraft, your allocated memory is probably being used up. Next time it gets laggy, press F3 and check in the top right to see if the percentage of allocated memory that's being used up is close to 100%. If it is, and you can't add more memory without crashing, then you need more computer memory. Simply search up "How to allocate more memory minecraft (insert minecraft version)" and you should find that there.
If the second issue is what you experience, it's one of three things. One, your internet is being slow. Two, you are located a significant distance away from where the server is hosted. Or three, the server is legitimately experiencing lag. It can even be a combination of all three. If your connection in tab is on a full five bars, and everything is delayed, then it's the server. To test your connection go
here. Speedtest isn't completely accurate, but it gives you a general idea. What you want to see is a low ping, high download speed, and decent upload speed. So under 50 ping, over 10 download speed, and over 5 upload speed. Try checking multiple places to see just how far your internet goes without slowing down significantly. Canada/United States is a good place to start.
I myself do not experience any of these issues anymore. The only time I did was back when I had a toaster PC with only 2GB of ram, a slow processor, and slow internet. Progress is necessary for a server, and sometimes new additions can cause the server to lag. Like you said, if it is the server, our admins are working hard to reduce lag. The lag could even be caused by a combination of both types of lag. I hope was able to offer some insight to possible lag and some solutions. If you have any questions just ask. I may have missed a few things due to the fact that I'm only speaking from personal experience, so feel free to correct me. ;P
