We used a new generation of asymptotic giant branch (AGB) stellar models that include dust formation in the stellar winds to find the links between evolutionary models and the observed properties of a homogeneous sample of Large Magellanic Cloud (LMC) planetary nebulae (PNe). Comparison between the evolutionary yields of elements such as CNO and the corresponding observed chemical abundances is a powerful tool to shed light on evolutionary processes such as hot bottom burning (HBB) and third dredge-up (TDU). We found that the occurrence of HBB is needed to interpret the nitrogen-enriched (log (N/H) + 12 > 8) PNe. In particular, N-rich PNe with the lowest carbon content are nicely reproduced by AGB models of mass M ≥ 6 M⊙, whose surface chemistry reflects the pure effects of HBB. PNe with log (N/H) + 12 < 7.5 correspond to ejecta of stars that have not experienced HBB, with initial mass below ˜3 M⊙. Some of these stars show very large carbon abundances, owing to the many TDU episodes experienced. We found from our LMC PN sample that there is a threshold to the amount of carbon accumulated at AGB surfaces, log (C/H) + 12 < 9. Confirmation of this constraint would indicate that, after the C-star stage is reached, AGBs experience only a few thermal pulses, which suggests a rapid loss of the external mantle, probably owing to the effects of radiation pressure on carbonaceous dust particles present in the circumstellar envelope. The implications of these findings for AGB evolution theories and the need to extend the PN sample currently available are discussed.