Thanks for the update, we unfortunately cannot see anything that would currently be causing these issues, so it may possibly be related to your internet connection. Chat should be stable at the moment, and there should also not be any major lag, as far we can tell at this time. A few Null systems are on a slightly more loaded node, which means they may occasionally experience some TiDi, but nothing that would cause lag.
This page contains some suggestions for troubleshooting these sorts of issues, which may help you out: https://support.eveonline.com/hc/en-us/articles/201827699-Network-communication-between-your-computer-and-the-EVE-Online-server-has-been-interrupted-