Apart from the university exchange programmes offered by UNIL, it is possible for students to pursue their studies abroad independently for one or two semesters, including at universities that are not UNIL partners (this special non-exchange status is commonly referred to as "free movers" or "guest student", although other terms also exist).
In this case, however, you will need to find out all the information and complete the formalities (admission criteria, financial conditions, producing your study plan) etc. with the host university yourself and you will not receive any administrative or financial support from UNIL.
Nonetheless, it is essential to have your study plan approved before you depart, by the mobility adviser in your faculty or section/school so that the ECTS credits you earn abroad can be recognised and/or to obtain equivalences. This can be a more complicated process than if you go to study under an exchange agreement.
The application deadline will depend on the host university you choose.
Submit your application to: host university.