All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If the woman’s Wali (guardian) abandons the prayer out of denial, then he has committed an act of disbelief according to the agreement of the Muslim jurists. Hence, he is not eligible to be her Wali in the marriage contract because being a Muslim is one of the eligibility requirements for the bride's Wali.
Allah, The Almighty, Says (what means): {…and never will Allah give the disbelievers over the believers a way [to overcome them].} [Quran 4:141]
However, if he abandons the prayer out of laziness, the jurists differed regarding the ruling on his situation. The majority of the scholars held that he is not a disbeliever, contrary to the most known opinion of the Hanbali scholars.
Based on the opinion of the majority of the scholars, his right to act as her Wali (in the marriage contract) is not waived, since uprightness is not among the eligibility requirements for the bride's Wali according to the preponderant scholarly opinion.
We would like to point out that this Wali must be advised and informed of the gravity of abandoning the prayer and the evil consequences of such an act. It is better to seek the help of some scholars and virtuous people to undertake this task, since their advice is more likely to be effective and fruitful.
Allah knows best.