There might be a big difference between "ideas" and "lessons", but perhaps you are referring to the assumption that the g'mara gives preference to earlier p'sukim over later ones when choosing prooftexts.
For example, Tosafos assumes that a pasuk from Vayikra should have been preferred over one from Yirmiyahu by default in the discussion of monetary transaction sources on Kidushin 2.
והא דלא מייתי קנין שנכתב בתורה
מכסף מקנתו (ויקרא כה) משום דבעי לאתויי קנין לשדה
Another possible example of this (once again, exemplified by its absence/exclusion) is that Rava should have preferred to teach how to interpret the Torah's legal round numbers (as in "40" == 39) from a pasuk in Vayikra rather than the one in D'varim that he chose. See for example this sheet.