Mary Logan (Jean Parker) is accused of murdering a blackmailer (Uncredited) who threatens to tell her boss, Mr. Gregory (George Irving), that she was the daughter of Tom Logan, a racketeer he prosecuted. It's up to psychologist/criminologist Charles Finch (Lionel Atwill) to connect the dots when the police take the easy way out and arrest, try, convict, and sentence her to execution. Once he figures out who really dunit he and Mary's sister (Marcia Mae Jones) race against the warden's wall clock to get the governor (Uncredited) to postpone the execution while Mary's girlfriend Dr. Dwight Bradf
You can stream Lady in the Death House (1944) free and legally on OldReel, via the Internet Archive.
Yes — it is in the public domain and can be watched and shared freely.