Shaw suffered the horrendous injury on Tuesday as United slipped to a 2-1 reverse to PSV Eindhoven on Matchday One in the Champions League.
The former Southampton youngster was taken off on a stretcher and was supplied with an oxygen mask, and the left-back was reportedly reduced to tears in the dressing room after learning the full extent of his injury.
Our thoughts go out to @LukeShaw23, who has suffered a double fracture of the leg. He will have an operation on his return to Manchester.— Manchester United (@ManUtd) September 15, 2015
United manager Louis van Gaal confirmed that Shaw has suffered a double fracture - as reported by the BBC - and he has since undergone surgery in the Netherlands ahead of a return to Manchester.
Former Chelsea star Lampard, who currently plies his trade for New York City FC in MLS, played with Shaw at the 2014 World Cup for England, and the ex-Blues midfielder has tipped his old teammate to return from the harrowing episode a stronger player.
Lampard told Sky Sports News: “It’s a terrible thing and we all hate to see that, especially because I know him and I know he’s good lad. He’s started his career really well and I know he’s only going to get better throughout.
“I’ve seen the reaction online and at home and he’s come out and said his recovery starts here and I can only say it’ll make him stronger, and I’m sure it will do.
"He’s a young kid and he’s got a long time ahead of him and he’ll come back and be an England international and a Manchester United player for many years to come.”
A recent report by Sky Sports has claimed that Shaw will have a second operation on the leg on Friday, and United plan on flying their player back to the UK should the surgery prove successful.
Meanwhile, the 20-year-old will be offered psychological support to help deal with the after effects of dealing with such a serious and lengthy injury.
A club source told the Daily Star: "Part of the recovery process will involve the player dealing with his mental demons and the bad memories of what happened to him that night.
"A psychologist will be made available to him if needed, to talk him through it all and help his chances of being mentally ready to return to the game."
Van Gaal's men return to action when they travel to Shaw's former club Southampton on Sunday afternoon.