You tried MusicIO? It allows bi-directional multi-channel audio and MIDI over the lightning connector. I don’t use it any more as I have my iPad hooked up to its own interface (greatly preferably IMO) but I seem to remember MusicIO working well! Although I’m not sure if it has its own keyboard or if you’d have to load one inside of it.
The other one is TouchOSC, which I had working over WiFi once but I don’t think it does Lightning.
Have you looked at duet? It’s an app that shares your MacBook (or PC) screen with your iPad. You can move the interface of a VSTi to the iPad and play its keyboard. Doesn’t work with iPhone. There are obviously loads more uses for it as a second screen for your laptop. Duetdisplay.com
I’m very new to the Mac/iPad world, so bear this in mind. Duet refreshes the iPad display at up to 60fps, and as far as I can see that’s what determines how anything on the iPad screen responds. You’re not using the iPad cpu to drive your vsti, the vsti remains on your Mac or PC and just the gui is moved to the iPad. You can get the iPad display to either mirror the Mac/PC, or create an extended display (which is what you’d do for this sort of application of Duet). It cost me £7.99 from the UK App store, I can’t remember if they do a trial version.