There is no European evidence that Lapu Lapu personally killed Magellan and there are first-hand accounts from Magellan's men of how he was killed at the engagement at Mactan. Here is a list of most of the main primary sources that are available online. Of the two or three that give accounts of Magellan's death, they all basically agree but Pigafetta's is by far the most comprehensive, although the shorter ones give a few extra details that are missing from Pigafetta. The only notable disagreement between them is in the number of Lapu Lapu's men; Pigafetta says 1,500 while the anonymous Genoese pilot says 3-4,000 and Maximilian the Transylvan says 3,000.

This is Antonio Pigafetta's account (starting at paragraph 99):

Friday, the 26th of April, Zula, who was one of the principal men or chiefs of the island of Matan, sent to the captain a son of his with two goats to make a present of them, and to say that if he did not do all that he had promised, the cause of that was another chief named Silapulapu, who would not in any way obey the King of Spain, and had prevented him from doing so: but that if the captain would send him the following night one boat full of men to give him assistance, he would fight and subdue his rival. On the receipt of this message, the captain decided to go himself with three boats. We entreated him much not to go to this enterprise in person, but he as a good shepherd would not abandon his flock.

We set out from Zubu at midnight, we were sixty men armed with corslets and helmets; there were with us the Christian king, the prince, and some of the chief men, and many others divided among twenty or thirty balangai. We arrived at Matan three hours before daylight. The captain before attacking wished to attempt gentle means, and sent on shore the Moorish merchant to tell those islanders who were of the party of Cilapulapu, that if they would recognise the Christian king as their sovereign, and obey the King of Spain, and pay us the tribute which had been asked, the captain would become their friend, otherwise we should prove how our lances wounded. The islanders were not terrified, they replied that if we had lances, so also had they, although only of reeds, and wood hardened with fire. They asked however that we should not attack them by night, but wait for daylight, because they were expecting reinforcements, and would be in greater number. This they said with cunning, to excite us to attack them by night, supposing that we were ready; but they wished this because they had dug ditches between their houses and the beach, and they hoped that we should fall into them.

We however waited for daylight; we then leaped into the water up to our thighs, for on account of the shallow water and the rocks the boats could not come close to the beach, and we had to cross two good crossbow shots through the water before reaching it. We were forty-nine in number, the other eleven remained in charge of the boats. When we reached land we found the islanders fifteen hundred in number, drawn up in three squadrons; they came down upon us with terrible shouts, two squadrons attacking us on the flanks, and the third in front. The captain then divided his men in two bands. Our musketeers and crossbow-men fired for half an hour from a distance, but did nothing, since the bullets and arrows, though they passed through their shields made of thin wood, and perhaps wounded their arms, yet did not stop them. The captain shouted not to fire, but he was not listened to. The islanders seeing that the shots of our guns did them little or no harm would not retire, but shouted more loudly, and springing from one side to the other to avoid our shots, they at the same time drew nearer to us, throwing arrows, javelins, spears hardened in fire, stones, and even mud, so that we could hardly defend ourselves. Some of them cast lances pointed with iron at the captain-general.

He then, in order to disperse this multitude and to terrify them, sent some of our men to set fire to their houses, but this rendered them more ferocious. Some of them ran to the fire, which consumed twenty or thirty houses, and there killed two of our men. The rest came down upon us with greater fury; they perceived that our bodies were defended, but that the legs were exposed, and they aimed at them principally. The captain had his right leg pierced by a poisoned arrow, on which account he gave orders to retreat by degrees; but almost all our men took to precipitate flight, so that there remained hardly six or eight of us with him. We were oppressed by the lances and stones which the enemy hurled at us, and we could make no more resistance. The bombards which we had in the boats were of no assistance to us, for the shoal water kept them too far from the beach. We went thither, retreating little by little, and still fighting, and we had already got to the distance of a crossbow shot from the shore, having the water up to our knees, the islanders following and picking up again the spears which they had already cast, and they threw the same spear five or six times; as they knew the captain they aimed specially at him, and twice they knocked the helmet off his head. He, with a few of us, like a good knight, remained at his post without choosing to retreat further. Thus we fought for more than an hour, until an Indian succeeded in thrusting a cane lance into the captain's face. He then, being irritated, pierced the Indian's breast with his lance, and left it in his body, and trying to draw his sword he was unable to draw it more than half way, on account of a javelin wound which he had received in the right arm. The enemies seeing this all rushed against him, and one of them with a great sword, like a great scimetar[187] gave him a great blow on the left leg, which brought the captain down on his face, then the Indians threw themselves upon him, and ran him through with lances and scimetars, and all the other arms which they had, so that they deprived of life our mirror, light, comfort, and true guide. Whilst the Indians were thus overpowering him, several times he turned round towards us to see if we were all in safety, as though his obstinate fight had no other object than to give an opportunity for the retreat of his men. We who fought to extremity, and who were covered with wounds, seeing that he was dead, proceeded to the boats which were on the point of going away. This fatal battle was fought on the 27th of April of 1521, on a Saturday; a day which the captain had chosen himself, because he had a special devotion to it. There perished with him eight of our men, and four of the Indians, who had become Christians; we had also many wounded, amongst whom I must reckon myself. The enemy lost only fifteen men.

The anonymous Genoese pilot's account that gives a few extra details can be found here (paragraph 12):

The second-hand account of Maximilian the Transylvan that gives a few extra details can be found here (paragraph 200):

From these you can see that Magellan seems to have been killed by many anonymous warriors working together. If Lapu Lapu himself had been there and delivered the killing blow, I think it probably would have been recorded by the Spanish but it wasn't. Lapu Lapu himself is in fact not mentioned anywhere as being personally involved in the fighting, although he might have been.

As to judging the reliability of these accounts, Laurance Bergreen, the author of Over the Edge of the World: Magellan's terrifying circumnavigation of the globe brings up the possibility that Pigafetta and others who were present at Megallan's death might have retreated from the battle without orders, leaving Magellan to be killed. So rather than being a heroic last stand, he was betrayed by his own men and they might have warped details of his death to suit this narrative. Many of Magellan's crew were extremely disgruntled by his extreme bravado in engaging in these native conflicts that he had no reason to even be involved in (and as you can see in Maximilian's account, he wouldn't even let his native allies participate and just wanted them to observe). This seems plausible since just over a year earlier, there had already been a very bloody mutiny against Magellan in March 1520, and there would be still more violent infighting and betrayals amongst the crew after Magellan's death.