Further, she did not initially describe Oswald as "short, a little on the heavy side," with "somewhat bushy" hair.

I have looked at the transcript, which includes the following...

Mr. Lane. Well, would you say that he was stocky?

Mrs. Markham. Uh, he was short.

Mr. Lane. He was short.

Mrs. Markham. Yes.

Mr. Lane. And was he a little bit on the heavy side?

Mrs. Markham. Uh, not too heavy.

Mr. Lane. Not too heavy, but slightly heavy?

Mrs. Markham. Oh, well, he was, no he wasn't, didn't look too
heavy, uh-uh.

Mr. Lane. He wasn't too heavy, and would you say that he had rather
bushy hair, kind of hair?

Mrs. Markham. Yeh, just a little bit bushy, uh huh.

Mr. Lane. It was a little bit bushy.

Mrs. Markham. Yes.

(Emphasis mine)

She said he was short, not too heavy, and his hair was a little bit bushy.

...according to her, he misrepresented himself as an official of the Dallas police when he called. Also, she testified that he had called her at work, and she was attempting to end the conversation as quickly as possible, so that she wouldn't get into trouble. This would explain her attempts at mild agreement with Lane's statements--e.g., telling him what she thought he wanted to hear, in order to get rid of him (note that this could have been a sub-conscious reaction). Finally, a detective testified that Mrs. Markham broke down when Oswald was brought into the line-up room.

Markham first claimed that she never even spoke to Lane, then claimed it was not her voice on the tape. So then she claimed that Lane misrepresented himself as a police officer. Strike three - the tape recording itself proves that Lane did not misrepresent or identify himself as a police officer. So this is hardly a valid supposition to dismiss her "...mild agreement with Lane's statements...in order to get rid of him...". And even if Lane had said he was a police officer, that explanation is absurd.

As for "lying," she initially claimed never to have spoken with Lane because, according to her, he misrepresented himself as an official of the Dallas police when he called.

Already discussed above. She lied about never talking to Lane, she lied about her voice not being on the tape, and she lied about Lane misrepresenting himself as a police officer.

Finally, a detective testified that Mrs. Markham broke down when Oswald was brought into the line-up room.

Ah, the lineup. What does she say to the WC about identifying Oswald?

Mr. BALL. Did you recognize anyone in the lineup?
Mrs. MARKHAM. No, sir.

Mr. BALL. You did not? Did you see anybody--I have asked you that question before did you recognize anybody from their face?
Mrs. MARKHAM. From their face, no.

Mr. BALL. Did you identify anybody in these four people?
Mrs. MARKHAM. I didn't know nobody.

Mr. BALL. I know you didn't know anybody, but did anybody in that lineup look like anybody you had seen before?
Mrs. MARKHAM. No. I had never seen none of them, none of these men.

D'oh! She has repeatedly stated she didn't identify or recognize anyone. Better 'suggest' who she is supposed to have seen before. So out of nowhere, we get the following banter....

Mr. BALL. Was there a number two man in there?
Mrs. MARKHAM. Number two is the one I picked.
Mr. BALL. Well, I thought you just told me that you hadn't--
Mrs. MARKHAM. I thought you wanted me to describe their clothing.

LOL! Let's see if this could be all a simple case of misunderstanding!

B: "Remember the number two man?"
M: "Oh, right, I picked number two!"
B: "But you just said you hadn't..."
M: "Oh that? I thought you kept asking me if I had seen any of their clothes before!"

Mr. BALL. Did you recognize anyone in the lineup?
Mrs. MARKHAM. No, sir.

Mrs. Markham must have thought he actually said...

Mr. BALL. Did you recognize anyone's clothing in the lineup?
Mrs. MARKHAM. No, sir.

Mr. BALL. You did not? Did you see anybody--I have asked you that question before did you recognize anybody from their face?
Mrs. MARKHAM. From their face, no.

She may easily have thought he said...

Mr. BALL. You did not? Did you see anybody--I have asked you that question before did you recognize anybody's clothing from their face?
Mrs. MARKHAM. From their face, no.

Mr. BALL. I know you didn't know anybody, but did anybody in that lineup look like anybody you had seen before?
Mrs. MARKHAM. No. I had never seen none of them, none of these men.

She probably heard...

Mr. BALL. I know you didn't know anybody, but did anybody's clothing in that lineup look like anybody's clothing you had seen before?

And she probably meant to reply...

Mrs. MARKHAM. No. I had never seen none of them, none of these men's clothing.