Lubrication of the movement is particularly important to reduce the friction and thus to be able to put a thinner and thus longer barrel spring for a longer power reserve. Also it will prolong the longevity of the movement.
In the adjustment part as well as in the movement part more in general there will be different quality of grease or oil used. In general, but with some exceptions, the emptier it runs, the more liquid the lubricant must be and vice versa. Also, in mechanical movements there is a point that will not be lubricated it is the two jewels of the axis of the anchor.
One of the most important lubrication points will also be at the pallets but between these two pallet-stones and the escape-wheel. It is often at this point that the lubrication deteriorates first and that the movement will then need an overhaul. This is why a lot of research has been done at this level, for example with the George Daniels escapement or the new silicon components that can theoretically work without lubrication.
At the level of the balance, we will put the most fluid oil that we put in a watch movement. Be careful to respect the right proportions of this lubrication which will often be done in two anti-shock.
As far as lubrication is concerned, it should be noted that quartz movements are largely unlubricated. The reason is that their gears work without the pressure of a spring so there is much less friction than on a mechanical watch and lubrication would not be adequate.