My favorites are Yonac’s ToneStack and Positive Grid’s BIAS FX.
It is also a bit complex to set up, so we’ll choose a dedicated app that’s just plug and play. The free option is GarageBand for iOS, which features a section dedicated to amps and guitar effects. You’ll need an app to actually process the digital signal and send it out to the speaker. You may notice that not much is happening. It has pretty much everything you’ll ever need.
Yonac’s ToneStack sounds fantastic, and works on your iPad and your iPhone. Some of these Lightning interfaces use the iPhone’s headphone jack as an output, which is fine as long as it has one. The guitar gets plugged into the big hole, your external speaker or headphones get plugged into the little hole, and the Lightning cable runs to your iPhone or iPad.