Bring vinegar, water, honey, and salt to a boil in a small saucepan. Remove from heat.
Put radishes, mustard seeds, black pepper, and bay leaf in a pint jar with a lid. Pour hot vinegar mixture over the radishes. Let the radishes come to room temperature. Cover with lid and place in the refrigerator for at least 2 hours.
Mix coarse sea salt, furikake, and sesame seeds together in a small bowl to create the seasoning mix.
Toast bread until lightly brown, about 2 minutes. Top each slice with half the avocado. Top avocado with a portion of the pickled radishes. Sprinkle half the seasoning mix over radishes. Place a small handful of cilantro on top. Squeeze lemon over the toast.