An aging, solitary cable car is the village's lifeblood, but the lease is up for renewal in 2017 and the community fears for the future.
Locals worry a big-business operator -- interested purely in profit -- will take over and destroy the soul of this unique alpine niche resort.
However, La Grave is struggling. People are moving away, and there's a tacit acknowledgment that investment is needed to revive fortunes.
"Everyone is afraid of the unknown," says Pelle Lang, a Swedish guide who owns the Skiers' Lodge
in the village. "There are a lot of people who have spent many years here, and it means a lot to them because La Grave is a special place."
The tiny 12th-century village in France's Ecrins National Park gives access to acres of adventure on the flanks of La Meije, a wild and remote 3,984-meter (13,071-foot) mountain, some 60 miles southwest of Mont Blanc.
No room for cruisers
This is no place for "blues cruisers" -- skiers who prefer intermediate pistes that offer limited challenges. There's one short groomed slope.
The rest is a mountainscape of glaciers, cliffs, crevasses, couloirs and forests -- and a dream for free skiers and their guides when the conditions are right.
"It is just an incredibly unique area and a special place, not only for skiing, but ski touring alpinistes, mountain bikers in the summer and farming," adds Lang, who pioneered the region as a hardcore skiing hub.
The only way up is via a 40-year-old cable car which takes 40 minutes to chug up via two intermediary stations from the rugged village at 1,480 meters to a high point of 3,200 meters.
There's one other lift, a rudimentary drag next to the single ribbon of piste high up on the glacier, rising to 3,530 meters just below the Dome de la Lauze.
The extensive ski resort of Les Deux Alpes lies just over the ridge. It's another world, of commercialization and big business, but one that threatens to engulf La Grave.
The lift has a capacity of 400 people per hour, and struggles to make money. The lift's designer, Denis Creissels, a man in his 80s, took over the lease in 1987 and runs the company at the margins of profitability.
For several years, rumors abounded that the lift would simply close when the lease ran out. The lift did stop for a spell in the 1980s when an earlier operator went bankrupt.
"I have had American clients ringing me up saying 'I want to ski La Grave because this is the last year the lift will run'," says Lang. "It has a bad reputation around the world."
However, six potential investors came forward and were whittled down to two by the mayor's office, with a final decision to be made in March. The identities of the two prospective leaseholders remain a closely guarded secret.
The worry among locals is that a mega lift company, such as Compagnie des Alpes, which runs many of France's top resorts including nearby Les Deux Alpes, Chamonix and Val d'Isere, will implement big changes to increase profitability and satisfy shareholders.
"Now, we as skiers adapt to the mountain," says Lang. "As soon as you start adapting the mountain to the skier, you're bringing bigger crowds and soon you have a bigger demand for services."
Locals are not "anti-development," but they're wary that turning La Grave into a slick resort will rip the heart out of an authentic and pristine alpine environment.
The added fear is the village will be neglected in favor of unsustainable property development.
Belgian resident Joost Van Zundert launched a crowdfunding venture to protect what he calls "this special place" for the community.
It attracted €61,000 ($64,000) from 1,012 backers to raise awareness, with the private investment already lined up for the next phase, but his was one of the bids rejected by the town hall
"The worst-case scenario for me is an operator who doesn't develop the village life and just operates the lift and thinks about its profits, not the product itself," says Van Zundert, who relocated to La Grave in 2005.
"That could endanger the authenticity of the skiing."
La Grave is a serious mountain requiring specialist skills to negotiate its slopes.
Of the 23 "legendary routes" pictured on Lang's Skiers' Lodge website, 16 have a technical difficulty rating of "very serious" or "extremely serious."
There have been a number of fatalities over the years, including big-name American skier Doug Coombs who died after a fall in the Couloir de Polichinelle in 2006.
Not for nothing does La Grave have the second highest population of mountain guides in the world after Chamonix, at the foot of Mont Blanc.
"It attracts skiers from all around the world, experienced skiers and people who have a dream or ambition to ski there," adds Van Zundert, whose group will continue to lobby for the preservation of La Grave.
Boosting numbers, with enhanced lift and accommodation infrastructure, or by connecting La Grave into the lift system of nearby Les Deux Alpes, could engulf the village and attract visitors without the necessary experience and equipment.
But La Grave faces a delicate dilemma.
Without investment, the prospects are gloomy.
The situation has not been helped by the collapse of a tunnel on the road to La Grave, blocking the western access for almost two years.
The alternative, a winding four-hour diversion to the east, severely hit businesses, although the tunnel's re-opening this winter will give the village some much-needed "oxygen," according to Van Zundert.
"It's so difficult to make money here. And people are very tired living with this stress," adds Lang.
"The sad thing now is that many people are moving away from La Grave, schools are declining, it's been a tough time for people here."
Securing the future of the lift is vital, but the flipside is that big companies waving checkbooks at impoverished landowners could hasten the exodus and expansion.
Then again, one of the stipulations of the new lease will be to build a third stage of the cable car up to 3,600 meters, replacing the old drag lift, before 2021.
Not only will this allow easier liaisons with Les Deux Alpes but it's hoped it will extend the season and increase summer traffic.
"They've been trying to open the lift up for summer skiing since they built it but they have never been able to make any money," says Lang.
"But if there is a cable car up to 3,600 meters it will compete with the Aiguille du Midi in Chamonix.
"The view is stunning. You can see to Italy and the Monte Rosa, to Mont Blanc, to the Massif Central, Mont Ventoux..."
No artificial snow
Among the other terms of the lease: No new pistes will be allowed and artificial snow making will be banned to preserve the authenticity of the environment. Lift improvements could also clean up some of the old infrastructure on the mountain.
But locals worry some of these seemingly positive upsides will be lost amid big-money negotiations.
"We pray they will come up with a solution and a good long-term working relationship with either of the companies," says Lang.
Like much of its skiing, La Grave is on a precipice. Whether it lands on its feet remains to be seen.