Praise be to Allah, and peace and blessings be upon the Messenger of Allah. To proceed:
Belief in the heart alone is not sufficient for a person to have complete faith as a Muslim. Rather, true faith requires the belief of the heart, the declaration of the two testimonies of faith (Shahada), and acting upon what Allah has made obligatory.
Whoever believes in Allah and His Messenger is required to fulfill the obligatory duties, foremost among them the prayer (Salah), as it is the greatest pillar of Islam after the two testimonies.
As for someone who neglects Zakah, fasting, or Hajj out of laziness while still believing that they are obligatory, they have committed a major sin, and their faith is diminished. However, according to the stronger opinion held by the majority of scholars, they do not leave Islam.
Regarding the prayer, many scholars—and this is a strong opinion supported by the textual evidence—hold that whoever completely abandons it out of laziness has committed major disbelief (kufr akbar). The Prophet ﷺ said:
"Between a man and shirk and disbelief is abandoning the prayer."
He ﷺ also said:
"The covenant that distinguishes us from them is the prayer; whoever abandons it has committed disbelief."
Accordingly, faith increases through obedience and decreases through disobedience. It is not valid to claim faith while abandoning the greatest obligations that Allah has prescribed.
True faith is based upon the belief of the heart, the declaration of the tongue, and righteous actions. Therefore, belief in the heart alone is not sufficient while neglecting the obligatory duties. Prayer is the greatest of these obligations, and the Islamic texts indicate the seriousness of abandoning it, to the extent that many scholars considered completely abandoning it to be major disbelief.
And Allah knows best.