This would be fantastic if work allowed me to install one. Sadly, some of us work in locked down environments so resort to such silliness to get through the work day.
I'm sorry. that sucks. That's just stupid. I could see employers requiring you to use their password manager, but ugh, not allowing use of one is just gross.
That said, lastpass can work without any modifications to your local machine(i.e. it can work without any browser plugins even) tho it's not very fabulously integrated, it does work... Assuming of course they don't block access to the lastpass website and JS.