Liberty City is the city of earlier Grand Theft Auto games. In VI it belongs to Lucia's family history: the life her mother already wanted there, and that Lucia tries to force for herself in Leonida.
Rockstar has not announced that you travel to Liberty City. Until that announcement exists, the city is not part of the playable map.
The exact wording in Lucia's profile: she wants 'the good life her mom has dreamed of since their days in Liberty City.' That makes the city the family's past before Leonida. Liberty City has been the series' version of New York since Grand Theft Auto III and Grand Theft Auto IV.