To perform a Lucene search through the web service, you will need to define what field you are searching for.
In the below example we are searching an exact name. In the q-parameter, your query should look like:

^name:"My university Name Here"

In your browser this will appear as:

https://devel.atira.dk/apac_im_test/ws/api/522/external-organisations?q=%5Ename%3A%22My%20university%20Name%20Here%22