Complex sentence: The immediate problem is that she is on trial for her life, charged with murdering her former lover--if Lord Peter does not prove she is innocent, he will lose her before he even persuades her to accept his proposal of marriage.
Split into simpler sentences: The immediate problem is that she is on trial for her life, charged with murdering her former lover. If Lord Peter does not prove she is innocent, he will lose her before he even persuades her to accept his proposal of marriage.