Most leases have a personal obligor on them or some other form of secuity put up, there are many instances of sublets just for this reason.
Even if your place of employment went of business the landlord would be able to collect.
And, do you really believe that your work puts your company over the top? Or even comes close to doing so?
I am sure Trinity is making quite a bit of income, no different than any other landlord in the city. As far as it being tax exempt income, it depends if there is financing on the property and certain other factors. Even tax exempt organizations are subject to income tax at the regular corporate rates for unrelated income. You may be able to google and see if they file a 990T.