Stable Osu! (the other one) runs quite well on my notebook (it is old, but still works):
The next screenshot show the hardware usage when osu! is in stand-by (not playing nor downloading beatmaps...):

As you can see, the CPU and RAM usage is very low, so Osu! runs quite smoothly.
But when i launch Osu!lazer, the performance decreases to the point i can't play at all;

Please, notice the higher usage of CPU and RAM.
In both situations, i ran nothing but Osu! or Osu!lazer.
Is this because my old notebook will not handle Osu!Lazer or because Osu!Lazer still in development?
This is a known issue. Optimization is necessary.
A few things to point out:
As has been said above, stable is the result of years of intense optimisation. You will see a similar process happen on lazer once we are done bringing it to feature parity.
I believe this should be a lot better these days. We've both drastically reduced memory (in all but intense gameplay) and reduced CPU via reduced allocs and optimisations. There is also a single threaded mode for low power PCs like the one mentioned in this issue.
So, single thread mode makes lazer work more like stable? Does that mean input is dependent on draw frames?
That's correct
Most helpful comment
A few things to point out:
As has been said above, stable is the result of years of intense optimisation. You will see a similar process happen on lazer once we are done bringing it to feature parity.