It is possible to agree that Henry VII was in serious danger of losing the crown after 1485 due to rebellions like Lambert Simnel, Perkin Warbeck and Lovell. However, it is also possible to disagree with this statement because Henry held the two princes people were trying to pretend to be and Henry was also well prepared for these rebellions.
The Lovell rebellion in 1486 was the first of a series of rebellions Henry faced. It consisted of 3 minor noblemen Francis Lovell and the Stafford Brothers. These all supported Richard and wanted to restore a Yorkist to the throne and wanted to oppose Henry's rule. Lovell was a threat to Henry due to the amount of support he had both nationally and internationally, this support included Margaret of Burgundy who could offer lot's of money, men and recourses to Lovell. Henry also feared that a country from France, Scotland or Ireland might profit from supporting the Yorkists attempting to reclaim throne so he was wary as he wouldn't be able to compete with these countries because he had no army and not much support as this rebellion was early in his reign as King.
However, some people believe that Lovell was never a serious threat to Henry as the King would have wanted to stop this rebellion relatively quickly so that he could stamp down his authority during the beginning of his reign, he did this by giving out harsh punishments to the opposers including executing Humphrey and arresting Thomas, he would have wanted this to be a deterrent so others wouldn't revolt against him. Henry also rewarded loyal nobles with land and titles and this would of helped him gain support throughout England only strengthening his support and helping him protect himself against these rebellions. The duration of the rebellion shows that it wasn't really a threat to Henry and that it was easily dealt with. This probably meant that other people were going to try different