I did everything right and when I stop the mini processor the dressing looks fine but as soon as I stir it I see it is separated. What should I d...

I was thinking along the lines of NOT blending the oils and acid (in this case, lemon juice) and just pourting them separately over the salad. That would give the same eventual tastes and maybe avoid the visual separation.
Or add more volume of emulsifier (garlic paste, dry mustard) and hope it coheres.
Found a fine article on why salad dressings separate, including suggestions of honey & tomato paste at emulsifiers. But I wouldn't use them in a Ceasar salad dressing.
So, again, maybe just emulsify the solids & fats, pour that and lemon juice separately over the salad, eat and enjoy.
https://www.sciencefriday.com/educational-resources/salad-dressing-science-emulsions/

Oh I'm so sorry Carla. It's never happened to me but I id find this article on Food52 that might help.
https://food52.com/blog/20807-how-to-fix-broken-salad-dressing-video
Please let me know how it goes....