What is the accusation towards Lenina in Brave New World? How was the Director embarrassed?

I think that what you are talking about here is the time
that the Director is saying that he is going to punish Bernard Marx by sending him to an
island.  He thinks that Bernard is being too unorthodox in his behavior, especially in
his sexual behavior.

The Director gets embarrassed (really
beyond embarrassed, maybe humiliated is the better word) when Bernard brings John the
Savage and his mother Linda into the room.

The fact that
the Director has had a child is beyond belief and humiliates
him.

I think that the accusation against Lenina refers to a
similar accusation -- that she is too sexually involved with Henry Foster instead of
being more promiscuous.