Lanette? No.
Mentor? Debatable.
Before Mentor came out, Fan club was the next best thing, it puts your pokemon on your bench just like Great ball, not into your hand... if that makes a difference in your world. Whether you want to waste the discard or not is a choice between 3 basics and 2. Fan Club also gets basics at ANY HP, not max 100 which is a big advantage and a reason why I consider it better.
Steven? No.
Most hands in Unlimited get past 7 cards naturally, it's nothing like Modified is where hand sizes are considerably lower. Remember Oak, Elm, Cleffa? 90% of Unlimited decks play a combination of those cards, almost all should play Cleffa. Those 3 cards are basically essential for Unlimited, if you dont use them then you'll lose by lack of quick draw. Item finder for Oaks and Elms brings you back to 7 cards too.