Cherry darkens naturally with age, more so in direct sunlight. The lye is not a dye or stain, just accelerates natural darkening, and doesn't hide figure of grain. Some recommended concentrations start with about 1 tsp lye (e.g. Red Devil powder/crystals) in 3 cups water. Leave on the wood for a minute or two, then wash with white vinegar to neutralize, then water to clean up. The 1 tsp/3 cups concentration may be a little tame. Experiment with stronger concentrations on some scraps from the same part of the tree for valid comparison. If lye is hard to find, or even if it isn't, consider oven cleaner (e.g. Easy-Off). Pretty much the same thing, but unknown concentration, and also has some additives which may or may not affect results. Again, experiment with scraps.
Wet treatment will tend to raise grain. Expect to re-sand afterwards, but don't go too deep or you'll reach untreated wood.
JG