Jesus said he was sent only for the lost sheep of Israel, so what is their destiny, according to Catholicism? Jesus said:


  I was sent only to the lost sheep of Israel. (Matthew 15:24)


It is safe to say he was rejected by the Jewish people (in general, excluding the few who may have believed he was legitimate)

This means who ever did not follow Jesus from the lost sheep of Israel are considered unbelievers and will be in Hell forever correct?

From a Catholic perspective.
"Israel" is more than the ethnic Jewish race, according to the New Covenant that was initiated by the death and resurrection of Jesus.  The name originates from the time the patriarch Jacob  wrestled with 'the' Angel and was renamed 'Prince of God'.  It became the identity of the nation that descended from the sons of Jacob, the 'twelve tribes of Israel'.  

John the Baptist asserted that God could raise up sons of Abraham from the stones, meaning that an Israelite could be defined by something other than his genetic code (Matthew 3:9; Luke 3:8).

The 'House of Israel' Jesus came to save referred to anyone who comes to God in faith, who believe in God's (not man's) plan of redemption through Jesus.   Paul goes on to state that ethnic Jews who rejected God's Son were removed from the tree of Israel, and their places were being taken by non-Jews who entered into the house of Israel by faith in Him (Romans 10).

The 'lost sheep of Israel' refers to anyone, Jew or Gentile, who recognized their separation from God, their powerlessness to change it through their own efforts (the law), and accepted God's gracious answer in Jesus.  "But to all who believed him and accepted him, he gave the right to become children of God." (John 1:12 NLT)