While Lucas, 24, has received the consistent backing of Liverpool managers, he has struggled to win over the fans since signing from Gremio in 2007.
However, his impressive performances over the last year have seen many supporters come around and, after he won his ninth cap for his country in the friendly against France this week, Dalglish feels he fully deserves international recognition.
"It was interesting to see him playing for Brazil on Wednesday," he said. "They have had some fantastic players in his position and the best known was Dunga, who won World Cups and went on to manage the national side.
"I've always said Lucas is highly thought of in Brazil, probably more than in Britain, but certainly not at Liverpool. I don't know why he has started playing so well. Maybe he just needed time to settle. Whatever the reason, we're just grateful for the job that he's doing.
"We have always appreciated what he can do. Last Sunday he was as good as anyone on the pitch at Chelsea, so to see him playing for Brazil wasn't really a surprise for me."
He added: "I don't think Lucas is going to be the one who beats five or six players and puts it into the back of the net, but he may be the one who stops the guy going past the first fella then sets us on our way.
"He's an important member of the team. Most teams have someone like that in the ranks and we are no different. The fact he started on Wednesday for Brazil tells you they must be very pleased with him as well, and the performances he's put in for us mean he's deserved it."