Lucas made his first appearance of the season in the 0-0 draw against Arsenal.
In his Liverpool Echo column, Aldridge said he would have been sad if the Brazilian midfielder left the club, as it was suggested that he would be able to leave Anfield after being left out of the matchday squad for the first two games of the Premier League season.
The ex-forward said: "He played well and, as I've said before, he can do a real job in that position, particularly against the bigger clubs.
"Despite the comments from Brendan Rodgers after the match, there's still a lot of speculation surrounding the Brazilian.
"We'll have to wait and see, but for me he's a player we can't afford to lose.
"It would be nonsensical to let him go but, if he wants to play regularly, Lucas may decide to go regardless. That's down to him: it would a shame to see him go."
Lucas showed that he has some sort of role to play for the Reds this season, even if he did miss the first two games. When it comes to difficult away fixtures against the top sides, Brendan Rodgers feels there is a need for someone to play the holding midfield role, and the 28-year-old is the best player to play that specific role.
After the international break, when the difficult away games start again, it would not be a surprise to see him feature pretty regularly before the turn of the year.
Aldridge added that he was impressed with Jordan Rossiter getting some minutes under his belt, and that perhaps enhances the case for keeping hold of Lucas - having an experienced professional to learn from as well as the team benefiting from important top-flight know-how in the bigger games.