Same issue here.
I've been using Squarespace for 4 years now and this lagging just started happening maybe 6 months ago (or more). It really hinders productivity and I'm now having to write my blog posts in Google Docs and paste them into the blog page just to cut down on some of the lag time.
I cannot believe there isn't a fix for this.
I've cleared my cache and cookies, tried different web browsers (I use Firefox on Mac), and nothing has worked.
Hope there's a fix on the horizon.