In Acts 3, Peter and John healed in the name of Jesus Christ a cripple. Did the power of Jesus Christ alone heal the man, or was it the man's faith also? If the man had no faith, would he have been healed? Scripture says the man praised God after the healing, but was he a Christian to have faith? Jesus had just ascended to heaven. The man had sat at the gate for many years begging, so he was well aware of God in the Jewish tradition.
If you think the man would have been healed anyhow by the power of Jesus Christ, then how does that differ from the healing of Christ in John 4:50?
If you note the passage, he didn't know who Peter and John was. He didn't know they 'could' heal him, thus he was not seeking nor asking for it.. therefore was not looking in faith for it. What God did through Peter was based upon Peter's faith in what God desired him to do.
Now it doesn't tell us that the Spirit of God spoke to his heart and told him to do such.. but we KNOW that if the lame man had not requested of him (as was part of the culture for the beggars to laid before the temple to plead for aid), Peter and John would have continued on in. Thus something happened in the heart of Peter, at/during the man requesting for help.
He was praising God because of where he was, depending on the kindness of 'believers' of the Jewish faith to help aid him. From this we can conclude he himself was most likely a believer in the Jewish Traditions (at the very least) but again, he did not ask for nor expect healing.
Another interesting point here is that it is greatly possible if not plausible that Jesus himself would have passed by this man, and yet never healed him. We know that Jesus healed all in the cites but 'all' does not refer to everyone there in, but 'all that were brought to Him". And if I'm not mistaken (and I could be, it is later here) he healed in Jerusalem too. This man was not healed then, but we see that the reason for Christ not healing this man (IF He had passed by) is because God would do later through Peter.
So making a short point very long... While it is possible he had heard of the Christian faith, he himself was not a part of the Christian faith, nor was he looking to be healed by Peter whom, apparently in accordance to scripture the lame man didn't know. Yet it was in faith that Peter stretched forth his hand and according to A.T. Robertson Word Pictures shows us from the Greek:
Acts 3:7
Took him by the right hand (piasas auton tēs dexiās cheiros). Doric form piazō for piezō. Genitive of the part affected.
Peter had to pull him up on his feet before he would try to walk.
Thus it was the power of Christ alone that healed the man, working through the faith of Peter who acted in obvious accordance with the heart and will of God Father, through Jesus, by the Power of the indwelling Holy Spirit. The main point here is that as Christ did nothing a part from the will of God, nor do those of faith.