Diaz missed Sunday's 3-0 home win over Nottingham Forest and the team dedicated the victory to him with Diogo Jota (26) hoisting the forward's number seven shirt aloft after scoring the first goal.
While Diaz's mother was rescued, authorities in Colombia continue to search for Diaz's kidnapped father.
"Lucho (Diaz) is an incredible player and we knew that. But then you see him in the building and he's the person who always smiles so we really care about him," Lijnders told reporters on Tuesday. "We try to support him now as much as we can - a lot of things out of our hands
"Lucho is one of us. Putting the shirt up for him was a nice gesture - he knows we are here for him," Lijnders added. "How the stadium reacted was special as well - whole fanbase is behind him. Our motto is 'You'll Never Walk Alone.'"
Thiago is still not training fully with Liverpool's first team squad due to setbacks from the hip injury that has sidelined the midfielder since April.
"We miss Thiago I have to say, I miss him a lot," said Lijnders. "Can you imagine our midfield, our new players, then they have Thiago Alcantara in the middle as well? Guiding the others, his experience, the way he passes, the way he moves.
"We really miss him, but he will take time. He will not be available. He's an unbelievable professional, unbelievable guy. We hope to get him back soon."
Lijnders said the versatile Stefan Bajcetic (19) was also unavailable for the fourth round tie at the Vitality Stadium due to injury but he was looking forward to fellow midfielder Curtis Jones (22) returning from a three-game ban.
"Curtis, yeah, he trained yesterday, and how Curtis is, full of energy," he said. "Really happy how he's playing for the team and that he's available."
Liverpool have won a record nine League Cups, but lost to Manchester City in the fourth round last season.
They defeated Leicester City 3-1 in the third round last month, while Bournemouth beat Stoke City 2-0.
Klopp's squad are fourth in the Premier League on 23 points after 10 games, three points behind leaders Tottenham Hotspur.
Bournemouth are 17th and just a point above the drop zone.
