The best way to get to the hotel from Lime Street station is by taxi. Ask for the Herculaneum Bridge Hotel or "Peglegs". The address is:

The Herculaneum Bridge Hotel
28-30 Herculaneum Road
Riverside
Liverpool
L8 4TY

Telephone: 0151 727 6211

Alternatively, the hotel can be reached by Merseyrail. After leaving Lime Street turn left towards the Adelphi Hotel. At the Adelphi cross over in to Hanover Street. Central station is signposted on the left after about 100 yards, just before Bold Street. Catch the train with final destination Hunt's Cross (the trains run every 15 minutes or so.) Alight at the first stop, Brunswick station.
On leaving the train, walk up the stairs and turn left through the doorway. Turn right and follow the road up to the left past the "Grove" minimarket. Turn right and follow the road past Boughton's furniture warehouse and then turn left up to the Herculaneum Bridge Hotel (5 minutes walk in total.) The reverse journey is of course an extremely convenient way of travelling into the City Centre!