A bookstore owner must re-live his father’s murder, stay alive, and protect his friends when the murderer escapes from an asylum transfer.

By "relive," do you mean he has to experience the murder from his father's perspective?

>> must re-live his father's murder.

Loglines should focus on the dramatic problem to be solved NOW, in the present tense. ?The dramatic problem NOW is to apprehend and/or kill the murderer. "Re-living the murder" -- whatever that means -- is old business ?Maybe it's a complicating factor in the story proper but it is extraneous for the purpose of a logline.

Loglines should emulate the experience of reading the script, re order the elements in your logline so they replicate the sequence of events in the story.
For example:
After his father's killer escapes an asylum, a fearful book-store owner must kill him in order to save his family.

I changed your action description "...stay alive..." is vague and a given, and "...re-live his father's murder..." confusing - the reader won't understand what that actually means.