When I listen to Japanese people speak, I usually hear them say ないで{HLL} and なくて{HLL}, with the pitch drop always placed on な, no matter the verb. But I might just be hearing things wrong.
However, I would assume that the pitch accent pattern for these forms change depending on the verb you use, depending on whether it's accented or not.
For example, for unaccented verbs, it would be ないで{HHH} and なくて{HHH}. And for accented verbs, the pitch drop would be where it usually is when the ない form is used (e.g., for the verb 食べる{LHL}, you would say, 食べないで{LHLLL} and 食べなくて{LHLLL}).
So, what exactly is the rule for these forms?