That's a pity, I know one of the overhead railway carriages is in the Museum of Liverpool but as a kid I remember the (world) Museum also had a number of trains on display but have no idea if any of them are still there since the museum was updated. Doesn't seem to be an accessible area anymore.
No, the transport section that used to be in the museum is no longer available. The overhead railway carriage and Lion were transferred to the Museum of Liverpool, but I'm assuming most of everything else was taken into storage.
On a side bar, Merseyrail absolutely sucked balls today. 12.30 to Southport was cancelled on the Northern line, so I had to get the bus into town for the New Brighton train. Then coming back, the 4.23 AND 4.38 were both cancelled. A 777 came in, let off its passengers, and we all got on board - only to be asked 2 minutes later to leave the train as they attempted to fix an unspecified fault.
The way the driver was bullshitting the passengers, telling them they were hoping to get the train working again in 10 minutes stuck in my craw. I knew he was just stalling, waiting for the next train to come in so we would all have to board that instead. Would have been quicker for me to get the bus back.