Yes you can apply for an FHA Loan - you will need to apply and qualify for a 203k Rehab Loan. That is also an FHA product whicht will allow you to complete the rehab or fixing up that the home you select requires. As for the down payment assistance program throught the City of Lowell, they will just require all the documentation and contracts that prove you are applying for that type of loan. That will allow you to accomplish that goal of buying a fixer upper and use the down payment assistance.
Please contact me directly if you wish to discuss the matter further, where I have the experience and contacts you need to obtain both the 203k Rehab Loan and the down payment assistance program.