Lucy wants an “Italian haircut”, a shorter style. The relevant portion of the clip begins at about 2:10 and ends at 3:00.
Transcript:
Lucy: You know what I’m going to do? I’m going to get an Italian haircut.
Ricky: Oh no you’re not!
Lucy: Why not?
Ricky: Because I like your hair the way it is.
Lucy: But it would look so good short. Please?
Ricky: Look… for my son’s sake, no.
Lucy: What do you mean for your son’s sake?
Ricky: I’ll ‘splain.
Lucy: Ok. ‘Splain.
Ricky: All people in the world are divided into two groups… men and women.
Lucy: [sarcastically] I know. It’s a wonderful arrangement.
Ricky: Now. Men have short hair, and women have long hair. That’s the difference between them.
Lucy: Oh?
Ricky: Now, I don’t want my son to be confused. He should know whether he should call you mother or father.
Lucy: [walking away] Oh… men! You make me sick.
And later at 13:45 in the video…
Ethel: Well, it’s a terrible thing to say about anyone, but I guess Ricky’s just a man.
Against All Evidence 
Does she end up getting the haircut still and then getting spanked for making a decision on her own? Ugh, yuck.
Ricky: Now. Men have short hair, and women have long hair. That’s the difference between them.
Poor ‘Ricky’, do you think we should let him know what the actual differences are, rather than stupid cultural conventions?
Two biogs for Lucille Ball, an amazing woman:
http://www.imdb.com/name/nm0000840/bio
http://www.essortment.com/lucille-ball-biography-20822.html
Ball took out a loan for $3 million and bought her ex-husbands half of Desilu. At the time, Desilu was the world’s largest production facility and Lucy’s take-over made her the first woman in history to hold such a position.
Though she played a ditzy, wild hearted redhead, in real life, Ball was nothing of the kind. In 1967, she sold Desilu Productions for $17 million, netting some $10 million.
And a snippet from elsewhere:
How did Lucille Ball change the television industry?
Lucille Ball changed the television industry, she was one of the first people to be pregnant on television, she was one of the most famous comedic women, and she was in one of the first television series to use more than one camera angle.
Every time I go get my hair cut (I like to keep it short and off my neck) without fail I will be asked if my boyfriend is okay with this. Usually jokingly, but it is still always asked.
So, I once asked my boyfriend if he cared if I got my haircut because after being asked for the 5th time about it my natural anxiety started to kick in and I couldn’t stop thinking about how my 50s greaser pompadour was going to rip us apart. My boyfriend gave me a look like I was crazy and said it was my head, who was he to tell me how to cut my hair. Or how to dye it. Or how to style it.
On the other hand, my mom let me style her hair the other day (also short but usually styled in conservative poofy curls) so I gave her a fauxhawk and she used one of my nose rings as a fake piercing. My dad wasn’t all that amused by it. When my brother came to visit and asked if this was a permanent thing my dad was like, “Of course it’s not! I don’t think I could stay with her like THAT!” Not sure if that was all joke or only mostly joke, but it’s really sad that something as stupid as a hair style and a piercing would change that much about how you viewed someone you supposedly love.
I don’t think it upset my mom as much as it upset me, mostly because it was just silly dress up to her and she wasn’t gonna continue to do her hair like that. But I noticed and I really kind cared.
Another way that Lucille Ball was pretty revolutionary: despite Star Trek getting tons of accolades for the first interracial kiss, Lucy and Ricky kissed pretty regularly on the show. (And they looked happy to be doing it, unlike Kirk and Uhura who were under some form of mind control, IIRC.)
I’d never actually watched I love Lucy before. I might track some down, a twelve minute clip wasn’t enough for me to make my mind up!
“If we wanna stay married we’re gonna have to go thru life with our heads in a rut”
Oy.
lol