In recent LO version (7.1 at this times), the Writer’s simple search UI (i.e. defaulting to a specific toolbar at the bottom of the window) is quite similar to the one provided in Firefox for example, but sadly is missing one of it’s best feature : incremental searching (i.e. the search starts as soon as you type).
This has been reported: https://bugs.documentfoundation.org/show_bug.cgi?id=140805