Can I fly a practice LNAV approach with an iPad?
In the US, there are no regulations prohibiting you from using an iPad for navigation while flying VFR. There are also no regulations specifying what equipment you must use for a practice approach. The key to this is that it is a practice approach. Therefore, it is flown VFR. Even if you were an IFR-rated pilot in an IFR aircraft under the hood/foggles, your safety pilot would be VFR.
If you fly that same approach IFR (whether IMC or VMC), then it is an actual approach even when done as a practice approach. Just the ATC expectations are changed. Flying IFR would require the proper TSOed navigational equipment.
One word of caution would be that this might not be a safe practice flying solo. It would be best to have your iPad mounted somehow to make it hands-free. You should also practice this with your CFI (preferably) or a safety pilot first.
It would also be unwise to have to switch back and forth from the approach chart to your Foreflight  AHRS screen on the same iPad. You are in a critical phase of flight. Doing what you plan would be an unnecessary distraction and a violation of the Part 91 sterile cockpit strong recommendation (not a regulation for Part 91, yet). Either print your approach charts or carry two iPads.
Some guidance for practice approaches is provided in AIM 4-3-21.