Combine finely flaked tuna with lemon juice, Japanese mayonnaise, and spicy mustard in a bowl. Set the mixture aside.
Heat the olive oil in a large skillet or wok over medium-high heat and cook the chopped red onion for about 5 minutes until it turns translucent and tender.
Add the shredded cabbage to the skillet, stir continuously for 2 to 3 minutes until warmed through.
Pour in half a cup of water, cover the pan, and allow the cabbage to steam for 5 minutes.
Remove the pan from heat and fold in the tuna mixture, mixing thoroughly to blend all ingredients.
Transfer the salad to a serving bowl and chill it in the refrigerator for approximately four hours to let flavors meld and cool.
When ready to serve, garnish with a Japanese soft boiled egg if desired, and season with salt and black or white pepper to suit your taste.