I am using the trial version of Lightroom 4.1.
I will soon be purchasing the full version 4.0 from Amazon, as it is cheaper than Adobe.
I will get a box from Amazon that I assume will contain LR 4.0.
Will I be able to just enter that 4.0 license key into my trial LR 4.1 or do I need to purchase 4.1 from Adobe?
The LR4 serial number is valid for all 4.x versions.
Just enter the serial number from your boxed LR4 version from Amazon into your Trial of 4.1 and you're good to go.
I suggest you take a minute to also register the software online with Adobe (it's part of the procedure when you insert your serial number) for future reference so that Adobe will know that you have purchased LR4 and you can retrieve the serial number in future.