Daniel Sturridge opened the scoring for the hosts nine minutes in before wasting two further first-half chances.
The England forward miscued another opportunity from close range just after the break but slotted home his second goal on 64 minutes.
Lucas was adjudged to have tripped Erik Lamela and Vincent Janssen stepped up to convert the penalty with 15 minutes left, but Liverpool—losing finalists last term—held on.
Lucas told Sky Sports: “Last year we came very close, but we don’t have any European [games] this year and hopefully we can win all three competitions.
“It was very good experience for [the young players], and they will develop.
“I think the manager showed the trust that he has in the squad and I think it was the right decision.”
He said: “It’s a nice feeling [to be back], but I’m grateful to god for helping me get through all the things I’ve had to go through and I’m happy with tonight.
“We had a lot of chances, we played some good football, so I think we deserved it in the end.”