Lifesense can detect Elementals... but probably not Golems
Unfortunately, Alive doesn't seem to be formally defined in Pathfinder. Generally speaking, however, there are 4 states of "being"
*In some places, it's implied that Dead is also a type of Object, but that's not directly relevant.
Elementals definitely fall under the "Alive" bracket. However, in many ways, Constructs (including Golems) are treated as Objects.
Furthermore, James Jacobs weighed in that he considers Creatures with a Con Score to be Alive. James Jacobs' rulings aren't official but tend to be pretty accurate (and are widely used because he is one of the more vocal Paizo employees on the forums). This is in line with the formal definition used in D&D 3.5e.
In this case, I think it follows that they would not be detected. Sure, they were "granted life their magical life via an elemental spirit" but it doesn't specify that they are "housing" the elemental and magical life doesn't sound like what Lifesense is intended to detect.
Unless you want them to be. You're the GM... if you like the lore that Golems can be detected by the trapped elemental (but not other Constructs), go with it.