What is a good thesis statement for a character analysis of Lady Anne in Shakespeare's Richard III?
In writing a thesis statement for anything, the content always depends on your position or opinion.
Because I do not know how you feel about Lady Anne in Shakespeare's Richard III, I can only provide you with a sample of how you might structure your thesis statement.
I would imagine there are two major standpoints one might choose from with regard to Lady Anne: is she loyal to her dead husband (Edward, Prince of Wales) and father-in-law (Henry VI) and ultimately worn down by Richard to marry him? Or, is she a foolish woman who is easily duped by Richard, forgetting about his part in the murder of her husband at the end of Henry VI: Part III, and more recently, Henry VI?
There is a similar argument with regard to Gertrude, Hamlet's mother, when she marries her brother-in-law after her husband's death, in Shakespeare's Hamlet. The question is generally, "What was she thinking?" Hamlet himself asks his mother this question—how could she be married to such a fine man (Old Hamlet) and later lower her standards so far as to marry his brother, a man without nobility or greatness? The biggest difference between the two plays (in terms of the women) is that in Hamlet, Gertrude is unaware that her brother-in-law, Claudius, killed her husband, Old Hamlet.
The situation is quite different in Richard III. In Act I, scene ii, Anne grieves over the loss of her father-in-law, and her dead husband, aware that Richard is responsible for both deaths.
Be it lawful that I invocate thy ghost,
To hear the lamentations of poor Anne,
Wife to thy Edward, to thy slaughter'd son,
Stabb'd by the self-same hand that made these wounds! (8-11)
The question of what drives Lady Anne to take Richard as her husband can come only with studying her character: what she says, how she feels, and how she responds to the other characters and situations she confronts for as long as she is in the play.
As mentioned, it is impossible to advise you how to write a thesis statement without knowing how you feel about Lady Anne. If you believe she has been worn down by Richard's relentless attention, you might write something like...
Lady Anne, the widow of Edward IV and daughter-in-law of the newly killed Henry VI, is a woman who greatly loved the men she has lost. While a stronger woman might have been able to defy Richard's desire to wed her, Lady Anne resists until she can do so no longer.
If you adopt a viewpoint similar to this, then it is incumbent upon you to prove (with quotations from, and summaries of, the text) that Lady Anne is, in fact, weak. Your examples must clearly support your opinion with regard to Lady Anne. Only in this way can you credibly defend your feelings and convince your reader to see (as you do) the kind of woman Lady Anne was.
Whatever stance you take, once you write your thesis statement, make sure each paragraph of your essay (or paper) refers back to that statement: stay focused.