This recommendation is not applicable to alcohol extracted Lion 's Mane, because that extract is optimized for the alcohol-solubles and is best taken with food.
The main active ingredient of most medicinal mushroom extracts are water-soluble beta-glucans, though. These are very large macro-molecules with a high molecular weight; in fact a type of dietary fiber.
When taken orally, intestinal absorptive cells (enterocytes) facilitate the transportation of beta-glucans and similar compounds across the intestinal cell wall into the lymph, where they begin to interact with receptors of the immune system, activating a wide spectrum of immunological effects.
Due to their size beta-glucans do not pass the intestinal wall easily. To increase the chances of beta-glucan entering the blood-stream it's common sense to have as little 'competition' as possible present. So no solid foods or fiber-rich smoothies !
Research found that the absorption / therapeutic effect of beta-glucans is improved when combined with vitamin C (ascorbic acid). The type or amount is not important: 20 - 50mg of the cheapest type will do. See e.g. this article - a Google search for 'beta-glucan vitamin C' will return many more results.
Vitamin C will also improve the absorption of iron.
You can also use lemons or limes mixed with (ideally hot or warm) water, either shortly before or after you medicinal mushroom intake. Another way is to pour the content of the mushrooms into a cup of hot water and mix it, then adding a squeeze of lemon/lime juice.