Rizwan Naseer, the chief of the state-run Rescue 1122 service said that 20 people were killed and 40 others were injured in the R A Bazar area.
The injured have reportedly been rushed to nearby military and civilian hospitals.
Firing reportedly took place after the blasts.
The area has been cordoned off by the army troops and emergency has been declared in hospitals across Lahore.
Army troops are guarding the roads and entry points in the cantonment.
Media as well as civilians have been barred from going near the blasts sites.
Information on how the security arrangement could be breached by the attackers is awaiting confirmation.
So far no group has claimed responsibility for the attacks.