The Canaries have impressed in their first season back in the Barclays Premier League and victory on Saturday evening would take them level on points with the Reds, who are currently eighth.
Dalglish is full of admiration for Lambert, who was a player under him at Celtic, and reckons the Norwich board should back him with whatever finances they can muster.
"In the summer they spent money really well on players so I think Paul will be looking to progress again next year," the Liverpool boss said.
"I am sure he will be rapping on the [chairman's] door saying any money they've made should be spent on players to enhance what the players there have already done.
"The record he has got, there shouldn't be much time wasted from the Norwich people in saying yes."
While Dalglish has had a net spend of around £70million since taking over in January last year, Lambert's dealings have been considerably less.
One of the club's best deals, however, was just before Lambert arrived when predecessor Bryan Gunn captured striker Grant Holt for about £400,000.
The 31-year-old has 13 league goals this season, making him the second highest English goalscorer behind Wayne Rooney, and headed the equaliser in the draw at Anfield earlier in the season.
"No-one gets anywhere without working hard but it is nice to see the likes of Holt with his hard work getting rewarded," Dalglish added.
"For anyone to do well for their honest endeavour is always pleasing. But I hope he has a bad day Saturday."
Norwich and another of last season's promoted teams Swansea have secured their top-flight futures for another year and Dalglish believes that shows the growing strength of the npower Championship.
"I think those teams have been exceptional this season," he said.
"Swansea have been excellent and thoroughly deserve the great credit they have received for their performances and Norwich come into that category.
"The teams that have come up this season have probably been the most successful of any which have done so."