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Just to add onto this comment, it's thought that the Sun is slowly getting hotter and more energetic as it gets older and in approximately 1 billion years, the Sun will be hot enough to render the Earth uninhabitable for life as we know it.
In approximately 5 billion years, the Sun will reach the end of its life and expand into a red giant, swallowing up Mercury, Venus and potentially Earth in the process. Interestingly, once the Sun reaches this phase of its life, it could potentially warm up some of the outer moons enough for them to have liquid water, if they can hold onto an atmosphere of course.
Someone please correct me if I said anything wrong, I'm just a casual space nerd and not a professional astronomer.
Ran we starlift the Sun to make it last longer?
What does "lift" mean in this context? A web search turns up a Doris Day musical from 1951 which is kind of funny to think about but I'm guessing is not what you mean.
As for the general case of modifying the Sun - or any star - in some way, it's all but certain to need a huge number of resources (or amount of energy, or both), and considering the Sun is on the order of a million times larger than Earth, far more than can be obtained from Earth alone.
I mean, I'd like to be proven wrong and there's some exotic-physics way of causing the helium in the Sun to spontaneously turn back into hydrogen, but if that was easy, you'd expect that we'd see stars do that by themselves occasionally. We don't, which implies there would still need to be some kind of energy input required to get it started.
Without exotic physics, we'd pretty much need on the order of the energy that the star had output from birth up to that point, and if we had that, we'd be better off using that energy in other ways.
We could get all Earth life off Earth and into a self-sustaining, space-faring habitat with a minuscule fraction of the resources. We might be better off aiming for something like that.
https://en.wikipedia.org/wiki/Star_lifting