Salting last is the whole point of this dish. Mushrooms are over 90% water. Salt early and osmosis pulls that water into the pan, so instead of browning they boil in their own liquid. Browning is what builds the savoury flavour through the Maillard reaction, and with water present the pan cannot pass 100°C, so that reaction never starts.
Spreading them in a single layer and leaving them works for the same reason. Crowded or turned often, the steam is trapped and the temperature stays down.
Shiitake goes in for the synergy. White mushrooms are high in glutamate and shiitake in guanylate. Together they are perceived as far more savoury than the sum of the two, which is why less salt still tastes like enough.
The garlic gets 30 seconds because of allicin — heat-sensitive, and bitter once it scorches.
The lemon juice goes in off the heat. The acid flashes off in a hot pan.
If you are eating them for vitamin D, check the pack for "UV treated". Ordinary white mushrooms hold 0.2 µg per 100 g; treated ones hold 26.2 µg.
Washing is fine. A brief rinse takes up only around 2% of their weight. Just do not leave them soaking.