Can he be alone with a woman to lead her in prayer?

It is not permissible for a
man to be alone with a woman who is not his mahram. 

The Prophet (peace and
blessings of Allaah be upon him) said: “No man should be alone with a woman
unless there is a mahram with her.” Narrated by al-Bukhaari (5233) and
Muslim (1341). 

And he (peace and
blessings of Allaah be upon him) said: “No man is alone with a (non-mahram)
woman but the shaytaan is the third one present.” Narrated by Ahmad (178)
and classed as saheeh by al-Albaani in Irwa’ al-Ghaleel (1813). 

These ahaadeeth are general
in meaning and indicate that it is haraam for a man to be alone with a
non-mahram woman under any circumstances, even if that is for the purpose of
prayer. The scholars have stated that this is forbidden. 

Al-Nawawi said in
al-Majmoo’ (4/174): 

Our companions said: If a
man leads his wife or a mahram of his in prayer, and he is alone with her,
that is permissible and is not makrooh, because it is permissible for him to
be alone with her when not praying. But if he leads a non-mahram woman in
prayer and is alone with her, that is haraam for him and for her, because of
the saheeh ahaadeeth which I shall quote below insha Allaah … then he quoted
the ahaadeeth that we have mentioned above. End quote. 

It says in al-Mawsoo’ah
al-Fiqhiyyah (19/267):  

The fuqaha’ are unanimously
agreed that being alone with a non-mahram woman is haraam. They said: No man
should be alone with a woman who is not his mahram or his wife, rather she
is a non-mahram, because the shaytaan may whisper to them when they are
alone, inciting them to do that which is not permitted. The Prophet
(peace and blessings of Allaah be upon him) said:  “No man is alone with a
(non-mahram) woman but the shaytaan is the third one present.”  And they
said: If he leads the non-mahram woman in prayer and is alone with her, that
is haraam for him and for her. End quote.