Hernandez limped out of Swansea City's defeat against Manchester City on New Year's Day with a hamstring strain.
Lamah came off the bench to replace the Spanish international in that game — and then picked up a groin problem.
The news that both players are out is a heavy blow to Laudrup given that he was already without another of his frontline wingers, Nathan Dyer.
Dyer is due to return towards the end of January after suffering ankle ligament damage at Norwich City on December 15.
And it now seems that Hernandez, whose Swansea career has been marred by a succession of injury problems, and Lamah, who had been enjoying his best spell since arriving in Wales a year ago, will come back into contention around the same time.
Until then, however, Swansea must rely on Wayne Routledge and Alejandro Pozuelo — who is happier in a central role — to deliver on the flanks.
Striker Alvaro Vazquez could be an emergency option, while right-back Angel Rangel has occasionally been deployed further forward by Laudrup.
But the injuries to Hernandez and Lamah are only likely to increase Laudrup's desire to add another wideman to his squad.
With Michu also on the injured list, Swansea's forward options are looking decidedly thin as they prepare for Saturday's Premier League trip to Manchester United, plus the home clash with Tottenham Hotspur eight days later.
Swansea may also be short of attacking players for their FA Cup fourth-round tie, which is due to take place on the weekend of January 25-26, plus the league game with Fulham on January 28.
Laudrup indicated even before the injuries struck that he was keen to add a new wide player to his squad, and Swansea are in discussions with Blackpool over Tom Ince.
Manchester United's Wilfried Zaha has also been touted along with Liverpool's Iago Aspas.
Another player who may be on Swansea's radar is Benfica winger Ola John.
The 21-year-old, younger brother of former Fulham forward Collins, is tipped to leave Benfica on loan this month having struggled to get regular game-time with the Portuguese heavyweights.
He joined Benfica for 9 million euro in the summer of 2012 having shot to prominence at Dutch club FC Twente, where his form saw him earn a Netherlands cap.
John signed a five-year contract when he went to Portugal, and the deal reportedly includes a 45 million euro buyout clause.
But there are suggestions that Benfica are prepared to let the versatile winger head out on loan.
Liverpool have also been touted as potential suitors, though reports in Holland suggest Ajax are the favourites to secure John's signature.
Swansea have also been linked with a move for Dundee United's 19-year-old left-back Andrew Robertson.
Everton boss Roberto Martinez watched United play at the weekend, and the Toffees and Swansea are said to be among a number of clubs interested in the Scotland Under-21 starlet.
"A number of English Premier League clubs have been in contact regarding Andy," said Robertson's agent, Liam O'Donnell.
"However, he will ignore the speculation and focus on continuing his development at Dundee United. He is perfectly happy at United."