All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If a Khateeb (the one giving the sermon) loses his ablution while giving the Friday sermon, there is no blame on him and he should proceed with the sermon without being required to do anything. Being in a state of ritual purity is not a condition for the Friday sermon. Al-Hajjawi said in Zad Al-Mustaqni‘: "Ritual purity is not a condition for the validity of both of them (i.e. the two successive sermons of Friday)."
When the Imaam completes the sermon, he has two options:
a- To authorize someone else to lead the people in prayer instead of him, since it is not a condition that the one who gives the sermon be the one who leads the prayer. The author of Zad Al-Mustaqni‘ said, when completing the aforementioned statement: "It is not a condition that the one who gives the sermons be the one who leads the prayer."
b- To perform ablution after completing the sermon and then lead the people in prayer. This does not affect the validity of his actions as long as the interval between the sermon and the prayer is not long. Ibn Qudaamah said in Al-Mughni: "Consecutiveness of the Friday sermon and prayer is conditioned. If the Imaam needs to restore his state of ritual purity, he can perform ablution and then offer the Friday prayer as long as the interval separating them (i.e. the sermon and the prayer) is not long."
Allaah Knows best.