Smith, a veteran of the 1997 tour to South Africa and the 2001 series in Australia, was hoping to make it a hat-trick of Lions trips when Sir Clive Woodward announces his squad for this summer's tour to New Zealand in little more than a week.
But the Scotland international's selection is now in doubt with both he and Saints team-mate Andrew Blowers requiring scans after picking up injuries in the first half of Friday's defeat.
Northampton head coach Budge Pountney said: "Losing Andrew was a big blow because he's a very experienced Test player.
"We're waiting on the results from x-rays for him and Tom."
