I do see that Wycliffe’s himself wasn’t a rebellious figure, as far as I can see in his own words, he was against such a violance. But I sense that some of his arguments were directly against the taxation and in sense of accepting laymans as a part of religion; which King himself would never approve. With all contrast; can we claim that Lollardy was one of the vital elements of the rebellion? Any reccomendetion on issue are highly welcomed aswell!
Yes and no. On the one hand, Wycliffe himself opposed the revolt and it was contrary to his political interests to have anything to do with it. On the other, one of the revolts leaders, a priest from York named John Ball, preached Lollardy to the mob with some of his own modifications. I'm not sure this question is truly answerable, since it is not clear how widespread Lollardy was at the time, nor is it clear how much of Ball's preaching was actually inspired by Wycliffe's.
The Peasant's Revolt was started by a row over taxation but the target of the mob itself was the council of advisors that ruled the kingdom on behalf of King Richard II, who was still a child. In particular, they hated John of Gaunt with a (literally) burning passion. John was seen as the man who truly sat on the throne, and was undoubtedly the most powerful man in England. He was the head of the Knights Hospitaller in England and had a very nice palace called Savoy in London. John of Gaunt was, in addition to the most powerful man, also the most hated man. He was widely seen as corrupt and self serving; all those taxes for war with France does not seem to have improved the English military, but John did always seem to have some extravagant new jewellery. It is hard to overstate just how much the average Englishman c.1380 hated him. In London, the people routinely vandalised his standard and mocked him openly, and John rarely went to the city as regent for Richard II because there was a realistic chance that the people would attack him. During the revolt, the mob targeted assets he owned like the HQ of the Knights Hospitaller and the Savoy, which they blew up with gunpowder from his own armoury. Had John been in the city along with other royal advisors, he would certainly have shared their fate and been lynched.
As of the Peasant's Revolt in 1381, John Wycliffe wasn't yet recognised as a heretic. He had published treatises on government in the 1370s that had been highly critical of the Catholic Church that got him in a lot of trouble, but also gained him some prominent supporters. Pope Gregory XI had censured him in 1377 with a papal bull taking issue with 19 aspects of Wycliffe's beliefs and he was summoned before a council to explain his beliefs. 1377 was a year of serious peril for Wycliffe. Nevertheless, Wycliffe emerged unscathed and his support was only growing. Another council in 1378 failed to censure Wycliffe and his writings only grew more fervent and more popular despite the enemies he was making. At these councils he earned very significant supporters who could protect Wycliffe from his enemies in any number of ways: John of Gaunt and Joan of Kent, who was Richard II's mother. The royal family at this time was not a fan of the papacy, and Wycliffe served their purposes. But through his association with John of Gaunt, he was unavoidably tied to the crown and its hated advisors. Wycliffe was not open about his theological beliefs at this time, and stuck to political statements against the wealth of the Catholic Church, which he saw as contrary to the teachings of the New Testament.
In 1381, Wycliffe decided to leap out of the heresy closet and announce his scepticism of the essential Catholic doctrine of transubstantiation. The University of Oxford accused him of heresy and Wycliffe's attempts to get John of Gaunt to come to his defence were falling on deaf ears, as even John was reluctant to involve himself with someone who was openly heretical. It was in the middle of these appeals to John that the Peasant's Revolt occurred. Note that, so far, Wycliffe's beliefs only apply to theology and the role of the Catholic Church in society, and had no bearing on the general social and economic hardships that motivated the rebels. The only clear link between Wycliffe himself and the Peasant's Revolt was Wycliffe's fondness for John of Gaunt, which placed him firmly on the wrong side of that revolt. So we might argue that Lollardy did not have much influence on the revolt because the movement's leader was on the side of the monarchy.
But even before he had been declared a heretic, Wycliffe's teachings were spreading fast and beyond his control. There was a preacher named John Ball who went from town to town preaching against inequality, including against the wealth of the Catholic Church. Before Wycliffe had even published his first criticisms of the church's wealth, Ball had apparently been locked up several times for his preaching. When he heard of Wycliffe, he was a keen supporter and incorporated Wycliffe's beliefs into his own preaching. Ball took Wycliffe's beliefs but added his own onto them, which included expanding Wycliffe's beliefs on Catholic wealth to the rest of society. Wycliffe did not have an issue with the power of the nobility - in fact his political survival was resting on it - but the logical conclusion of his teaching was that leaders in general should not horde wealth. John Ball took this and ran with it. According to the Historia Anglicana one of his sermons during the Revolt included the lines:
When Adam delved, and Eve span, who was then a nobleman? From the beginning all men were created equal by nature, and that servitude had been introduced by the unjust and evil oppression of men, against the will of God, who, if it had pleased Him to create serfs, surely in the beginning of the world would have appointed who should be a serf and who a lord"
And, just to make things clear, allegedly finished up by urging to followers to pursue
"uprooting the tares that are accustomed to destroy the grain; first killing the great lords of the realm, then slaying the lawyers, justices and jurors, and finally rooting out everyone whom they knew to be harmful to the community in future."
So looking at Ball, we might say that Lollardy incited the crowd to lynch the king's advisors. But it is difficult to tell how much of this was really Lollardy, and how much of it was Ball taking an idea he liked and spinning it to serve his own beliefs. Ball had, apparently, always held beliefs like this. When the Peasant's Revolt began he was sitting in a prison in Kent and was freed by the crowd. Those justices he wanted killed were the ones who kept locking him up for inciting public disorder; their mutual hatred went way back, long before Wycliffe entered the picture. To know how much the Peasant's Revolt was influenced by Lollardy, we'd have to know how much of Ball's preaching was inspired by Wycliffe and how much was inspired by his own personal hatred of the nobility. It seems the Lollards themselves didn't care much for acts of violent rebellion, or equality. Their issue was with the wealth of the Catholic Church, which they saw as antithetical to the teachings of Christ that they preached, but that's not an argument about equality, that's an argument about hypocrisy. The earliest coherent view we get of Lollardy from the Lollards themselves post-Wycliffe is the 1395 Twelve Conclusions of the Lollards that was produced as a placard nailed to prominent places, and its companion pamphlet Thirty Seven Articles against Corruptions in the Church, both of which remain focussed on the moral failures of the Church rather than on financial equality.
Another issue with quantifying the role of Lollardy is the issue of spread. Lollardy was literally months old when the Peasant's Revolt began. It didn't even have a name at the time. Itinerant preachers like Ball spread Lollard ideas very effectively, but it is unclear just how much of the English population had heard of it, let alone believed in it. This makes answering a question like "How much did Lollardy effect the Peasant's Revolt" very hard to answer, because we do not know how influential it actually was beforehand. Furthermore, one did not have to be a Lollard to hate inequality. Wat Tyler believed in the common ownership of all goods, property, and land - more of a proto-communist than a Lollard - and his movement would grow to be more associated with strictly political campaigns against inequality rather than the heresies of Wycliffe. For example, after the Peasant's Revolt the city of London threw its support behind the reformer John of Northampton as their new mayor with a promise of radical reform aimed at reducing inequality in the city. But John of Northampton was no Lollard, just a populist who saw inequality as corrosive to the sense of community that London prided itself on. There's no heresy in this, and frankly no theology at all to tie it explicitly with Lollardy. How many of the people who agreed with Ball did so because they were Lollards verses how many were just sick of their taxes being spent on John of Gaunt's extravagant wardrobe? Again, we have nowhere near enough information to know. I'm not sure your question can actually be answered, since it requires answers to questions that we lack the information to properly examine.
For academic reading, the only article I could find specifically on the relationship between Lollardy and revolts is Aston, Margaret E. "Lollardy and Sedition 1381-1431." Past & Present 17 (1960): 1-44. It's old but good, and remains commonly cited.