So my point is, this leaves us in our lifetime with an infinite supply of Bitcoin.
You cannot define something infinite and limit it to a certain time which in this case is our lifetime. Perhaps you can simply say we cannot mine all bitcoins in our lifetime.
I agree, infinite by it's own definition means no bounds or limits but bitcoin has which is 21 million thus you can't say it's infinite. Bitcoin nowadays is very hard to mine thus it may take a couple more years to mine all the 21 million so I agree with you about us not being able to mine all of it in our lifetime.