The first is Mark 10:46-50. This is the story of Bartimaeus a man who was blind. We are told that when Bartimaeus heard that Jesus was passing by, he began to shout "Jesus, Son of David, have mercy on me!" Jesus tells his followers to call him. When he came to Jesus, He asked him, "What do you want me to do for you?" That is an interesting question from Jesus. Because He had healed people, everyone in the crowd knew what the man wanted, no doubt including Jesus, yet he asks the question. Now we learn later after Bartimaeus says, "Rabbi, I want to see" that Jesus tells him, "Go, your faith has healed you" meaning that he was a man of faith. This is critical. A man who already has faith in Jesus, comes to him asking for mercy. Perhaps Jesus sees that he already has the most important thing, his faith, and that is why he asks what he wants.
In contrast, we can look at Mark 2:1-12 the story of the paralytic who is lowered through the roof. Interestingly, the passage says in verse 5, "When Jesus saw their faith, he said to the paralytic, 'Son, your sins are forgiven.'" He doesn't comment on the paralytic's faith as the reason for the forgiveness of his sins but rather on the faith of those who brought him. This raises many questions about this interaction and how it occurred. Did his friends just take him or did he want to see Jesus? Clearly the friends were men of faith. But Jesus doesn't ask him or his friends what he wants. He sees their faith and says to him your sins are forgiven. Now once again, it seems obvious, perhaps, why his friends brought him to Jesus. Maybe they were trying to develop his faith, but more likely they wanted Jesus to heal him of his paraplegia. The healing itself also appears to be the result of the thoughts of the teachers of the law who were present questioning Jesus' authority, not specifically because of the man or his friends. It is also noteworthy that the man once healed later in the story, doesn't say anything. He just got up, took his mat and walked out.
In both of these stories of interactions between Jesus and a person with a disability, it appears that LIKE ANYONE ELSE, the critical factor is their faith.