But it would seem 25-year-old Smith is homesick after moving south from Rangers in the summer.
"He is over his injury problem, but has an issue in that he's unsettled, which is a major issue at the minute," Lambert told BBC Radio Norfolk.
"Effectively I don't have three left-backs. Stephen will probably, in time, go on loan or go home."
Smith did not have the best of starts at Carrow Road, damaging ankle ligaments before the season started.
I just think its a shame that he hasn't settled as he looked quite good before he was injured
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And when an injury to Adam Drury in October finally gave him a chance of nailing down a first-team place, he suffered his own setback in the form of a hip problem.
That has helped restrict the Scot to just five starts for City and he is unlikely to add to that number.
"I'm not going to criticise someone for it, it can happen. When you move in football you can toss a coin whether it's going to be good or bad," Lambert added.
"Certain things in his own private life are private and if you can't settle somewhere it's difficult to turn it around, that's why I had to bring another player in."
Meanwhile, second choice goalkeeper Declan Rudd is likely to be out for a month after suffering a fractured jaw in a practice match this week.
Youngster Jed Steer, who has yet to play a senior competitive game but has experience at England youth level, will step up to the bench.
"He came with us to Germany [in pre-season] and did really fine, he's only a kid you've got to remember," said Lambert.
"But I think he's got the mentality to handle being around us which I think is a big thing for a young player.
"I don't need to call in cover unless something were to happen to John Ruddy."
Source: BBC Sport
Source: BBC Sport