Will there be any issues with the presenter wearing a lav while speaking into another mic (feedback)?
Simply, no. Feedback is caused by a microphone picking up its own sound from the speakers. Additional microphones which are not connected to the venue sound system simply cannot generate feedback in any way.
Unless the presenter is in custody and handcuffed to the lectern, putting a wireless lav on him/her is an excellent idea.
I’m concerned about the levels being far to high.
Recording from the venue sound system is also a good idea as a backup to your own (wireless lav) microphone. It is easy enough to deal with the levels and isolation from the house wiring with a simple isolation transformer and attenuator. I am very fond of the Rolls DB25b It combines the function of transformer isolation (to prevent ground-loop hum both in your system, and in the venue sound system) PLUS a variable attenuator so that you can handle ANY kind of level that may be available from the venue sound system.
https://www.amazon.com/Rolls-DB25-Matchbox-Direct-Ground/dp/B00102XXZG
———————————————————————————
Recording audio without metering and monitoring is exactly like framing and focusing without looking at the viewfinder.