The distance between you and the server locations are causing the lags. If you press TAB in Minecraft you can see the ping (latency) right next to your name. Five green bars would be great, the less you have the more lags appear. The ping is extremely important for lag-free playing. As you said, if the ping is too high you even won't be able to place or remove blocks. That's because you run into timeout on serverside with your requests to place/remove blocks. The lower the ping the better.
Example for a good connection, low ping. You should have few or even no lags:
Example for a bad connection, high ping. It's more likely that some lags appear if your connection status looks like this:
Please refer to this Minecraft forum post to see an example of the ping meter. Further I found this helpful website which shows Minecraft servers with the best ping at your location.
Having lots of FPS doesn't help you out in this situation. The frames per second is the amount of single frames (images) your graphics card can produce and send to your monitor in one second. Ping instead measures the round-trip time for messages sent from the originating host (you) to a destination computer (your minecraft server in the US) that are echoed back to the source (you again). If that takes too long you are getting asynchronous with the servers and the other players and you get lags. See this Wikipedia Article for more information about ping.
You could look for servers which are closer to you and which have lower pings.