1.  If he’s married and pretending to be single.  Trust will forever be impossible to establish.
2.  Undisclosed previous record of murder or violent outbursts.  Even this lie has not deterred some women.  Statistics have shown many lonely or latently aggressive women who have fallen in love and married incarcerated convicted murderers.
3.  Serial cheating.  I use the phrase “serial” because I believe on single episode of infidelity may be forgivable and can be helped to understand, repair, and move forward.  With the proper professional guidance, people can overcome this type of deep breach of trust when there are two willing partner and the Cheater genuinely feels remorse, regret, and empathy for his or her partner/victim.  I have rescued and saved many celebrity couples who experienced cheating/infidelity in their relationships.  Of course, I have treated many couples who did not survive.
4.  Lying/denial of parenthood/paternity when indeed it is true.
5.  Investing the couple’s entire savings/finances without consulting the other partner and all is lost.  Some couples survive this type of massive breach of trust.  I am current working with such a couple.  However, the anger, hurt, fear, and rage that must be confronted together is profound.  Many cannot bear and sustain expression of these powerful feelings.