Ever since Lammy's debut, she and Lumpy have been at ends, although there have been a few positive interactions between the two here and there.
Lammy appears to be enemies with Lumpy and disrespects his authority. In A Bit of a Pickle, Lammy refuses to stop driving when Lumpy, a police officer at the time, tried to chase her down, though this could have been Mr. Pickels' doing. But when he finally pulled her over, she acted openly defiant to the orders barked at her, showing disrespect towards his clear authority, and paying dearly for it. Similarly, but to a lesser extent to the above, in All Work and No Play, Lammy ignored the barriers Lumpy put up and she - along with Sniffles and Nutty - snuck into the demolition site Lumpy was working at while he was on his lunch break.
If one is quick to notice, there are two occasions where Lammy is shown indirectly interacting positively with Lumpy. In You're Kraken Me Up, Lammy can be seen in the background watching Lumpy try to save "Giggles" and later cheered when she appeared to be resurrected. To a lesser extent, in The Chokes on You, she and Mr. Pickels are seen eating at a doughnut shop that Lumpy works at.
Likewise, Lumpy has a very low opinion of Lammy, viewing her as a miscreant and even a criminal. In A Bit of a Pickle, he chased her down and tazed her in the eye before locking her in jail, though he was following his job as a police officer and was ethically justified in most of his actions. In All Work and No Play, he (incorrectly) decided she was dead from her injuries and gave very little concern for her, even twisting the steel bar in her head so that it matches his antlers, doing so again at the end of the episode. As a vampire, in All In Vein, Lumpy had presumably captured Lammy and Mr. Pickels; draining her blood as well as partially eating the pickle. After doing this, Lumpy crushed her body like a soda can and discarded it.
The only positive mark on Lumpy's opinion of Lammy is that in All Work and No Play, he initially showed concern for Lammy's injury, though this was very brief.
- Because of an April Fools joke, they both won Vote or Die.