What are some important facts, quotations, and events that take place in The Lion in the Winter?

I don't know what you mean by important facts, quotations,
and events that take place in the play, but I'll give it a
shot.

I'll begin with some of the facts.  It is a fact that
Henry Plantagenet and Elenore of Aquitaine were married and they had four sons.  By the
time play opens the eldest, Henry, is already dead.  That leaves Richard, Geoffrey, and
John.  Henry is the king of England and Elenore is his
queen.

When they met, Elenore was married to Louis, the
king of France.  The Pope annulled that marriage so that she could marry Henry.  She was
a very wealthy woman.  She was also a woman willing to take a risk.  She states in the
play that when she went to the Holy Land, she imitated the Amazon warrior women by
riding bare breasted.  This is true.

It is also true that
the two had a tempestuous relationship.  It was no secret that Richard was her favorite
and Henry kept her under lock and key because she had led a rebellion against
him.

It is true that after Henry's death, Richard aka
Richard the Lionhearted became king and was succeeded  by his brother, John.  This is
the one and only John to have ever ruled England.  He is the King John of the Magna
Carta.  Elenore, by the way, outlived her husband and saw both of her sons on the
throne.

As for the events in the play they are probably
fiction based upon facts.  Did this Christmas meeting take place?  Maybe, but the events
depicted in the play happen only on stage.  Was Richard betrothed to Alais?  Yes, but
they never married.   Henry was known for having affairs so the affair between Alais and
Henry in the play is quite possible.

Did Richard have a
homosexual affair with Phillip?  I don't know but it is possible and would explain why
Richard never married...or maybe the reason he never married is he was too busy making a
name for himself...or maybe, considering his role models, he just decided not
to.

As for important quotations, that is really up to
personal choice.  Since I once played Elenore, my favorite quotes are from her.   I
don't know how important it is but I had a good time saying it.  When Henry threatens to
get rid of her as his wife and marry Alais she attacks him with his age and time and
says, "How old is daddy then?  What kind of spindly, ricket-ridden, milky, semi-witted,
wizened, dim-eyed, gammy-handed, limpy line of things will you beget?" It was hard to
learn but fun to say.

On a more serious note, one of my
favorite Elenore lines is from this same scene (Act 2, scene1).  "Life, if it's like
anything at all, is like an avalanche.  To blame the little ball of snow that starts it
all, to say it is the cause, is just as true as it is
meaningless."

Hope that helps you.