"Finally Got My Stolen Purse!"

How it was stolen?

Let's recollect all the statements given by all accused.

Lilian:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it. 

Judy:
(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Margaret knows who did it. 

David:
(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it. 

Theo:
(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse. 

Margaret:
(13) I didn’t take the teacher’s purse.
(14) Judy is guilty.
(15) David can vouch for me because he has known me since I was born. 

Let's not forget that 2 of 3 statements made by each student are true & other is false.

Now, Theo says he is innocent in his 2 statements - (10) and (12). Since, 2 of his statements are true then (10) and (12) must be true. Hence, Theo is really innocent in case.

If Theo is innocent then both (3) and (9) are lie.

If (9) is lie, then other 2 statement of David i.e. (7) and (8) are true. If (8) is true then (15) must be lie. 

And if (15) is lie then both (13) [lie in (12) also suggests same] and (14) must be true. 

Hence, as per (14), Judy is guilty who has stolen the purse.