iPhone locked with old Apple ID.

You acquired your device second hand from someone other than Apple or an authorized Apple reseller. The information below explains what has happened. You apparently didn't know to heed the advice given below.

"Before you buy/acquire an iPhone, iPad, or iPod touch from someone other than Apple or an authorized Apple reseller, make sure that the device is erased and no longer linked to the previous owner’s account."

And see: Activation Lock for iPhone, iPad, and iPod touch https://support.apple.com/en-us/HT201365. See this heading Check for Activation Lock before you buy/acquire a device from someone else.

The presence of activation lock means that we can't help you. We are not authorized to remove the activation lock from any device. And, under your circumstances, Apple support will not remove it since you cannot provide proof of ownership that they will consider to be sufficient. You would need and have your purchase receipt for the device from an authorized Apple seller with the device's serial number on it. 

All I can suggest is that you try to recovery the needed password (or possibly the purchase price) from the party you acquired the iPhone from. Recovering the password is the only way the phone can be made functional for your use. And getting it from the person you acquired it from is the only way to so. In your case, the previous owner will need to use forgot your Apple ID or your Apple ID password to recover the needed credential.