The Dove is a symbol of both the Holy Spirit and the dove which brought Noah the olive branch after the great flood. The dove with flames is frequently used to represent the Holy Spirit, resting on the shoulders of believers at the time of Pentecost. The Lamb is one of those symbols which shows up all over the place. The Lamb holding the shepherd's crook is Jesus, the Lamb of God, the good shepherd. Frequently Jesus used symbolism of the lamb in his stories.
Lambs are agile.
Lambs provide the gift of wool. Lambs know the voice of their master. On an aside, in the Himalayan mountains I once watched a number of shepherds making camp with their sheep mingled. The shapers knew each other, made camp together, and went off their separate ways every morning in order to find enough grass for their sheep. At night, the sheep all slept together.