Hi there, sorry I'm late.
Your question seems to imply a misunderstanding of the timeline.
The People's Liberation Army launched their invasion/liberation of Tibet in October 1950. Tibet was then led under the name of Tenzin Gyatso, the Dalai Lama, who was only fourteen years old at the time. A Regency council functionally led Tibet in his name. After the PLA decimated the Tibetan army at the Battle of Chamdo, the Dalai Lama fled to Gyantse Dzong in the small Phari panhandle between Bhutan and Nepal (just in case). The surrender in Lhasa was called "The Seventeenpoint Agreement" and reportedly distressed His Holiness to hear that his country - without his input - had given in to the enemy.
Thus began just under a decade of attempts (the operative word) of Sino-Tibetan cooperation. For lots of detailed information on exactly how that cooperation worked out, I recommend Tsering Shakya's Dragon in the Land of Snows, the authoritative book on Tibetan history post-1950.^1
Rewinding just a bit, it serves to think about three things:
Dalai Lamas have left Tibet before, and bad things frequently happened. Lobsang Gyatso, the Fifth Dalai Lama, was the first to politically control all of Tibet. He left the country early in 1652 to meet the Shunzhi Emperor in China. It went pretty well, all things considered. But his successor, Tsangyang Gyatso, the Sixth Dalai Lama, was captured and taken prisoner across northeast Tibet (Amdo) to China (presumably for execution) and died en route.^2 The Panchen Lama left Tibet to visit the Qianlong Emperor in the late 1700s^3 and the contemporary fears of smallpox in China were well founded... the Panchen Lama died in China. Finally, the Thirteenth Dalai Lama, Thubten Gyatso, predecessor to the current Dalai Lama, fled to Mongolia during the British invasion of Tibet in 1904, and then (somewhat ironically) to India in 1910 when China invaded Tibet. So basically, the Dalai Lama only leaves Tibet if there's something very wrong and he's taking the last resort to set it aright.
Tibet is hardly a homogenous entity today, and was far less so in the past. In the '50s, when our story takes place, Lhasa had finished its state-building exercise, managing to coalesce a strong base of power in south-central Tibet, U-Tsang (Tib: dbus gtsang), and this, like most monarchies, was centered around the Dalai Lama as a uniting force. The Gelukpa school was large and powerful, but Tibet had five plus schools of Buddhism. The Dalai Lama was conveniently a multi-religious institution. The regions that had trouble being convinced that Lhasa was vested in their interests, Amdo and Kham, now had an Amdopa Dalai Lama to look up to. In short, the Dalai Lama was a symbol of the nation. If the Dalai Lama fled Tibet, Tibet flees with him.
The Chinese, as much as they promoted the "Five Races One Nation" idea, knew all of this. They knew that their position in Tibet would be fractious at best if the Dalai Lama fled, so they did everything (they thought) they could to keep him... short of giving him actual power.
To answer your question, the Chinese absolutely did not want anything bad to happen to the Dalai Lama. Beijing dreamed and aspired to show the Dalai Lama of the glories of socialism, hoping to even convert him to Atheism^4 by bringing him to Beijing in 1955, showing him the wonders of the modern world and the prosperity of socialist civilization. There in Beijing, Mao told the Dalai Lama that Tibet would be allowed to transition slowly to socialist paradise, while the rest of China (including Kham and Amdo which Beijing had separated from Tibet proper) would be accelerated into socialist paradise. The Dalai Lama reportedly returned to Lhasa excited with the idea that Mao understood him and wanted to work with Tibet and the Buddhists.
Well, 1956 happened. That year was the 2500th anniversary of the Buddha's Paranirvana and the Dalai Lama was invited to Bodh Gaya to celebrate. The Chinese were scared out of their mind that the Dalai Lama was going to use this opportunity to defect, though no source anywhere indicates it was on his mind. Also in 1956 the Khampas out in Eastern Tibet finally had enough of their land being redistributed and collectivized, and then being forced into collectives where inefficient farming was being led by Beijing bureaucrats who had no idea how agriculture, nevermind local agriculture, worked. Before the PLA could take away everything - including their very valuable guns - the Khampas took what they had left and launched a massive rebellion. Monks often gave refuge to the warriors, and the Chinese attacks on Buddhist monasteries now proved to the Tibetans that the Chinese were not here for liberation, they were here to destroy them and destroy the Dharma.
Things continued to unravel. The Dalai Lama returned to Lhasa and was put in charge of a series of committees that had no real power (or were dominated by Chinese former military, not Tibetan locals). Remember, he was the symbol of Tibet and Tibetan legitimacy, but his ability to help his people was continuously undermined, misportrayed, and ultimately destroyed. He found himself in the position where all he could really do would be to denounce the Khampa rebellion, or the Chinese. Either would ultimately speed the destruction of his nation. I discuss a here from a bit of a different perspective that he was working on his PhD at the time. Well, the Tibetan Buddhist equivalent of a PhD. He passed his final examinations with flying colors and the celebrations were marked for 10 March 1959.
con't