No.
What you have found is NOT a lie of course.
But where in that narration you posted is written that "disobeying your parents is disbelief"?
Edit:
Sorry my friend, you were right and I was wrong:
I found this passage:
One who doesn’t deal with parents good, he may loss his Iman during the time of death. It is narrated by Imam Ahmad that a man came to the Prophet (Pbuh) and said, “O Messenger of Allah, there is a young man named as Alqama here who is dying. He was told, ‘Say Laa ilaaha ill-Allah,’ but he could not say it. He said, ‘Did he not say it during his lifetime?’ He said, ‘Of course.’ Then the Prophet (Pbuh) sent for his mother who said that she was angry with him because he used to favour his wife over her. Then the Prophet (Pbuh) gathered firewood and told his mother that he would burn her son before her very eyes. She said, ‘O Messenger of Allah, he is my son and I cannot bear to see you burning him in front of me!’ The Prophet (Pbuh) said, ‘O mother of ‘Alqamah’, the punishment of Allah is more severe and long lasting. If you want Allah to forgive him, then forgive him (yourself). By the One in Whose hand is my soul, his prayer, fasting and zakaah will not benefit him so long as you are angry with him.’ So the woman forgave her son and after some time he died after uttering the shahaadatayn (twin declaration of faith).” Abu Huraira (Ra) related that the Prophet (pbuh) said, “There are four people who will not enter Paradise as Allah decreed: a drunkard, a usurer, he who appropriates the orphan’s property without a legal cause and he who shows disrespect to one’s parents.” (Al Hakim).
If this is a saheeh hadeeth, then that means that a person can indeed become a disbeliever if he disobeys his parents!!
the link:
https://www.daily-sun.com/post/27838...beying-parents