There is no immigration check when you leave the US. So, having a visa or not doesn't prevent you from departing.
However, since you are transiting in the UK, the airline will want to make sure that you are able to transit; and since you don't have a US visa on your new passport, you will need to obtain a UK transit visa if you want to get a boarding pass.
The other option is to transit through another country (by changing the airline you use). For example traveling on Emirates you would not need a transit visa as there are no airside transit requirements for the UAE.
Indian nationals can also transit through the Schengen zone without a visa.
You will need a visa stamped in your new passport or other proof that you are admissible to the US in order to avoid having to obtain a transit visa for the UK.
As you will also need a valid visa in order to board your return flight, you should arrange to have a UK transit visa applied on your passport.
Make sure you bring with you the police report that you filed for your stolen passport to the US embassy in India to obtain another visa stamp, so you can board your return flight and be admitted to the US.