I do not believe that suicide is a one way ticket to eternal damnation as the Catholic Church for example knows. I do though believe that a suicide can go to hell based on their works on Earth. For example, Hitler undoubtedly is frying.
The Catholic Church does not hold the view that suicide is a one way ticket to eternal damnation.
I am a Catholic who has lost a close family member to suicide. The Church's view is that suicide is a grave sin which, if done with full knowledge of the gravity of the sin and with full consent and not repented of, merits Hell as all unrepentant mortal sins do.
My view is that it's a very open question whether people who commit suicide possess the ability to fully consent to their actions, and another open question as to whether someone who commits an act which leads to their death has time and ability to repent before death. Only God knows of these things in any individual's case. As such, we should operate under the assumption that a person who committed suicide is in (a very long stint in) purgatory, and pray for their soul as much as possible. If they aren't in purgatory, there's no harm in praying for them anyway, and we can't possibly know either way in this life.
To be brutally honest, there have been times when I wished she was in Hell. The amount of pain she caused myself and everyone I love the most has been incalculable. On some level, it feels deserved, logical, necessary. A selfish atheist who commits suicide merits Hell if anyone does, no?
But there is an old saying that when tempted to think of God's justice, remember His mercy, and when tempted to think of God's mercy, remember His justice. The only thing which results from desiring damnation for another is to damn your own life to one of bitterness, anger, and resentment. Whether or not she's in Hell, I only build Hell here on Earth for myself and my loved ones if I can't find a way to forgive her and seek her best end. Ultimately, all I can do is trust that God will do whatever is most fitting, most just, and most merciful. And all I can do teach my daughters of the unhealing wounds she caused while I pray for her soul every day for the rest of my life.
