I am afraid you can't do that... the train from the airport is the R2Sud (sud=south) and it can take you to Passeig de Gràcia station but not to Plaça de Catalunya station. From there you can walk to Liceu, it's a nice walk and it's not too long (under a mile), even with luggage: http://bit.ly/2LJCOln
Should you prefer not to do that, at Passeig de Gràcia train station just follow the signs to transfer to the metro (L3, green) and take the next one towards Zona Universitària. Just two stops away (<10') you'll be in Liceu.
All of this you can do with a T-10 for 1 zone bought at either the booths or the ATM's at the train station in terminal 2 at the airport and both will count only as one journey -but you must insert the card into the validation machines twice, once at the airport and another when entering the metro premises in Passeig de Gràcia.
There are trains from the airport every 30', the metro, however, runs every 3 to 5 minutes.