Why do pre-main sequence stars show lithium in absorption?

As pre-main sequence (PMS) stars contract towards the main sequence, their cores become hotter.

Lithium is turned into helium by proton capture reactions. These are initiated in the core at temperatures of around 3 million K, so much lower than for hydrogen burning.

At the same time, PMS stars, or at least the type of low-mass pre-main sequence stars that are being referred to here, are fully convective and this mixes material inside the star rapidly and effectively.

Thus the sequence of events is that the PMS star contracts; the core reaches $3times 10^{7}$ K at some point before the main sequence; Li is destroyed by proton capture; the Li-depleted is completely mixed with the rest of the star.

In this way Li can be rapidly and totally destroyed on a timescale that depends on the mass of the PMS star. It is as short as 10 Myr for a star like the Sun, increasing to about 100 Myr for a star of $0.1 M_{odot}$.

That is the basic picture, but there is a wrinkle for stars with $M>0.4M_{odot}$, where the core becomes radiative rather than convective before they reach the main sequence, but after Li burning has commenced. The radiative core pushes outwards and its base then drops below $3times 10^{6}$ K. This means that although Li destruction runs to completion in the core, at least some Li can be preserved in the outer layers of such stars.

Li is therefore an extremely complicated function of age and mass. But for the purposes of identifying low-mass PMS stars we can clearly say that anything that shows strong lithium signatures is probably younger than 100 million years if it is below about $0.5 M_{odot}$ (or equivalently is a K- or M-type star).

If you want much more detail, see my review article on Pre-main sequence Lithium depletion.

The H$alpha$ emission of PMS stars is connected with their youth. It can arise in two ways. The first is associated with accretion from a circumstellar disc. This is caused by gas falling from the disk onto the star and heating up. The H alpha emission can be very strong and very doppler broadened ($>300$ km/s). As pre-main sequence discs only survive for 10 million years or less, then this is a very clear signature of a pre main sequence star.

On the other hand, young stars that have lost their discs also show strong (though not as strong as accretion-related emission) H$alpha$ emission that is caused by non-radiative, magnetic heating of their chromospheres. This magnetic activity is associated with convective, rapidly rotating stars. Pre main sequence stars possess both these properties. Thus PMS stars must exhibit H$alpha$ emission of some sort.