You lost me here. You were asked about the private key, and you are saying you got it from transaction information?!? What am I missing here?
From the transaction I got the public key related to the address 1LzhS3k3e9Ub8i2W1V8xQFdB8n2MYCHPCa.
You can get the private key from a public key only if you know already that the private key lies in a very limited range (in this case from 2^54 to 2^55)
Can you please explain the method you were using to accomplish this magic? 2^55 - 2^54 = 1.8 x 10^16, that's a lot of private keys to check by brute-forcing them. What you are claiming doesn't make sense at all.