The specific events here foretold occur are described in the trial sequences in the New Testament (see Matt. 26:62-63; 27:12-14; John 19:9-11; Luke 23:8-10, as noted in Ludlow 1982, p. 454).
The reference to the lamb is not simply a literary follow up to the previous verse, but a layering of symbolic meaning. The lamb as sacrifice for Israel comes from the Exodus:
Ex. 12:1-7
1 And the LORD spake unto Moses and Aaron in the land of Egypt, saying,
2 This month shall be unto you the beginning of months: it shall be the first month of the year to you.
3 Speak ye unto all the congregation of Israel, saying, In the tenth day of this month they shall take to them every man a lamb, according to the house of their fathers, a lamb for an house:
4 And if the household be too little for the lamb, let him and his neighbour next unto his house take it according to the number of the souls; every man according to his eating shall make your count for the lamb.
5 Your lamb shall be without blemish, a male of the first year: ye shall take it out from the sheep, or from the goats:
6 And ye shall keep it up until the fourteenth day of the same month: and the whole assembly of the congregation of Israel shall kill it in the evening.
7 And they shall take of the blood, and strike it on the two side posts and on the upper door post of the houses, wherein they shall eat it.
While the reference is not absolute since Isaiah includes a lamb before the shearers (an image of humiliation?), the death of a lamb combines symbolically with the bearing of the "iniquities of all" in a very powerful way.