Backups do not take locks. Full stop. End of story.

Yes, in my experience backups do usually have some impact on the system. To be honest that's pretty unavoidable. It is, however, possible for the impact they have not to cause problems with the application.

Get some benchmarks for your systems. What do things look like when the app's running fine? What do things look like during backups? What do things look like when other nightly processes are running? What do things look like when there's these timeout problems. The more data the better (to a point). Once you know what normal looks like and what abnormal looks like you can start digging into what causes the differences.