Is there a way to replace navbar search with ajax search?

[Jesper+ 1]

Hi there. 

I have a client requesting ajax live search in the navbar instead of the defauls search. I am aware that i can add it as a shortcode, in a widget, but the searchbar does not resize very well on smaller devices, and i would have to change a lot of styling to do so.  

Have anyone had any succes replacing this? The plugin i'm referring to is this: https://da.wordpress.org/plugins/ajax-search-lite/