Official Tung advice for parking. They suggest Paddington pay & display multi storey on Grove St with a special rate for up to 5 hours for users of the Tung.

“ 24-hour pay and display parking is available at Paddington Village Multi-Storey car park located at The Spine building, Grove St, Liverpool L7 3FA. The car park is approximately 4 minutes’ walk from the venue.

Tung Auditorium ticket-holders can park in Paddington Village and have their parking fee reduced to £5, for a stay of up to 5 hours. To use this offer, park as usual then on return press the information button on the pay machine and inform the member of staff you have been to an event here and they will reduce the parking fee to £5”

Additionally
There is a paying car park opposite the entrance to the underground Met car park and it’s quite cheap – pay on exit

This is what is on LMO website:

Tung Auditorium: Yoko Ono Lennon Centre, 60 Oxford Street, Liverpool, L7 3NY.

Official University visitor parking is here www.liverpool.ac.uk/maps/visiting/car-parking/

However, staff parking on Peach Street is usually free and accessible in evenings and weekends, 3 minute walk to venue, but consult signage as enter.  Barrier is normally up when free.