This sentence is ambiguous as it stands.
The first possible meaning is that you already know that that he found out about something some time ago, and you are speculating about what he found out and what he would do after finding out. It really is possible that the thing he actually found out that he was going to die.
The second possible meaning (although it's not the way it's phrase it), is that you are speculating about what he would do if, at some time in the future, he found out that he was going to die. This is a hypothetical situation.
If the second is what you want to say, your sentence would probably be OK in casual conversation but if you wanted to be completely clear in a formal situation it would be better to say
If he were to learn that he would die, he would love to get...
were to is only used in a hypothetical situation, so this is unambiguous.