I'm going to start with "this is SOOOOO stupid" first (the fact that east coast gets better ping on LAN than on NA).
That being said, all you're missing on LAN communication-wise is toxicity. I have an account on LAN, and most of the people say Baron (or something RREEAALLLLYY close to that), they say drag, etc. etc. So you can understand them for what's important.
As for you communicating with them, just communicate via pings. 1 ping = suggestion, 3 = you're telling them, 5 = you're going to rape them (I would stay away from 5 pings).
To SOME extent this is your ISPs fault (TO. SOME. EXTENT.). I had my internet service from Centurylink at my parents house, I moved in with a friend and got comcast, my ping on NA dropped by nearly 20... I moved all of 4 MILES! So, to SOME extent, it is your ISP. That being said, it's Riot's fault that the servers aren't more centralized to better accommodate the entire NA populace.
Oh, and if you're wondering, I get 90+ on NA, and 40-50 on LAN.