She could have found out who had killed Tarrlok-san. Whether it was an accident or not didn't matter, the culprit would be executed either way.

...it is possible the culprit panicked and killed Lynne-san in an attempt to cover their tracks.

We also can't forget the burned remains found in the incinerator, if the note said Tarrlok-san had suffered an accident - which may be true, his death could have been an accident - and Lynne-san went to investigate...

[In other words, he still suspects of Misa, as much as he dislikes that train of thought]