I think there are known issues with Dolphin Browser. Not sure if the issues are related to lag though. I rarely seen any lag using Swiftkey X. I've been using it before X and it's been great.
What phone do you have? On my old Optimus V, I would get lag in Dolphin and a few other apps so I'd often have to switch to the stock keyboard. I'm currently using the G2x and I don't notice any lag like I used to.
Yeah. I get a little lag every time the keyboard pops up. I wonder if its because since its not the stock one, the process needs to start up every time we click an empty field. I don't know, just my theory though.
If you have a task manager that kills (either automatically or manually) the Keyboard's background process, you will see a delay when pulling up the keyboard the next time. The first thing you should do after installing the keyboard (and after using it the first time) is set your task manager to not ever kill that process. It has fixed most of my keyboard lag on both Swift X and Hacker's Keyboard.
Is anyone using the latest Beta from the VIP program? They made a few enhancements, including a better heat map overlay so you know what's going on and the ability to increase the height of the keyboard from small, medium and large. It makes a huge improvement to have more control over the size of the keyboard, imo.