Yes, Lupron (leuprolide) can cause a sudden, severe decrease in blood pressure, though this is a rare side effect. Lupron can also cause general hypotension (low blood pressure).

Discussions on medical forums, such as the Mayo Clinic Connect, include patient reports of experiencing sudden mid-day drops in blood pressure and light-headedness while taking Lupron.

A sudden drop in blood pressure caused by Lupron can lead to serious symptoms. If you experience any of the following, seek immediate medical attention:
Fainting
Dizziness or lightheadedness
Fast or irregular breathing
Weakness
Trouble breathing