It is better to have a new receptacle, but you can make the old one work.
The receptacle has a cage around it on the backside. You can go to any autoparts store and look at one. The cage is threaded at the end of the receptacle, that's what pinches the dash and holds the receptacle tight. You can remove the cage, pull the receptacle out and push the "fingers" of the receptacle in to make the lighter fit tighter. Just test fit as you're doing this to avoid over bending the fingers.
I got a universal lighter receptacle from Napa and replaced mine. It was inexpensive and is working fine whether you want to use the lighter or phone charger / AC inverter.
This is similar to what I got:
The "cage" I'm speaking of is ground, you connect a spade terminal to the cage to ground it after you install it in the dash. The center terminal inside the receptacle is where you hook +12 volts, fused, either on all the time or keyed, your choice.