Is it permissible for one who did tayammum (dry ablution) to lead (in prayer) one who is in wudu?
Basically there's no harm if the Imam did tayamum as far as he had reasons for that. As among the reasons of tayamum there might be some kind of illness which doesn't allow him to wash or pure water on his skin.
Here's a quote of Ibn Hazm showing the views of scholars on the matter:
Ibn Hazam said: It is permissible for one who has done tayammum to lead in prayer people who have done wudoo’, for one who has done wudoo’ to lead people who have done tayammum, for one who has wiped over his socks to lead those who have washed their feet and for one who has washed his feet to lead people who have wiped over their socks, because each of those whom we have mentioned has done what he is obliged to do. None of them is more taahir (pure) than another, and none of them is more complete in prayer than another. The Messenger of Allaah (peace and blessings of Allaah be upon him) enjoined that when the time for prayer comes, the one who has most knowledge of the Qur’aan should lead them in prayer; he (peace and blessings of Allaah be upon him) did not specify anything other than that. If there had been any obligation other than that which he mentioned, he would have explained it and would not have neglected it – Allaah forbid. This is the view of Abu Haneefah, Abu Yoosuf, Zafar, Sufyaan, al-Shaafa’i, Dawood, Ahmad, Ishaaq and Abu Thawr. That was narrated from Ibn ‘Abbaas, ‘Ammaar ibn Yaasir and a group of the Sahaabah (may Allaah be pleased with them). It is also the view of Sa’eed ibn al-Musayyib, al-Hasan, ‘Ataa’, al-Zuhri and Hammaad ibn Abi Sulaymaan. (Source)
Note that the Maliki school allow it but consider it as makroh, while the Hanbali school says it would be better if somebody else who has performed the ablution/wudu would lead the prayer.
The Shia' view is already quoted by Muhammad.
And Allah knows best.
As much as I search, I figured out that apparently he can be Imam-al-Jama’a. I said that because I found a similar question/answer as it was saying that ... if he is canonically/Shar’an excused, he can be Imam al Jama’a by Tayamom Badal-al-Qusl. But I think for more being confident you can go to the source below.