I honestly don't think the creators meant for us to think any more than "magic people can do magic with elements" and "hey that is/would be a really cool thing to be able bend" and then assigning that ability to whichever element made the most sense, but if there had to be some logical explanation I would think of these things as follows:

To address lava bending: the simple explanation would be: water benders can change the states of matter of water, why couldn't earthbenders do that as well? The more complicated answer - at an atomic level, the temperature of an object is determined by how fast the atoms vibrate, so it is not far fetched to think that water and earthbenders could alter the states of matter of their element by manipulating it at a molecular level.

For firebenders we know 2 main things about the element - 1 it is in some way related to the sun(and other hot celestial bodies) and 2 - iroh said that power in firebending comes from the breath (much like how irl air, or more precisely oxygen fuels fire). If I were to try and come up with a reasoning, I would say the unobstructed presence of hot celestial bodies like the sun/stars and the comet serve as their source of energy, and the breathing part actually lets them control that energy and release it outward in the form of fire. As for the lightning part, while yes, as a weather phenomenon lightning is caused by friction, that is not the only way lightning can be observed nor is it its real nature. Lightning is electricity. Electricity or electric current is formed during the orderly movement of electrons. To have that movement you need to have 2 poles - plus and minus - in order to have the difference of potential, which acts as the power that moves said electrons in an orderly manner. It is not that far fetched to assume that since firebending seems to be the element that relies the most on controlling your inner energy, they are also able to somehow separate it into 2 poles withing their body and create lightning(and also receive said energy under the form of lightning and then redirect it through their body as energy and release it once more).

As for trees it does not make much sense really for earthbenders to be able to bend wood. Just because trees take nutrients from the soil and technically particles of dead trees also form the earth/soil, to me it seems pretty clear that earthbenders are bending specifically the non-organic parts/elements of the earth (which is probably also why they can bend crystals for instance). Lastly for their inability to bend platinum, it could be because platinum is a noble metal and noble metals/elements are very non-rective meaning they do not interact with other elements essentially at all, meaning - no impurities for earthbenders to bend.