The current icon is a reference to the phrase "green thumb," which means a natural skill for gardening. The hand on the new image only has four fingers and the thumb turns green, just like a regular zombie.
'Morticulturalist' is a combination of the word "horticulture," which means gardening, and the Latin root "morti," which means to have a relation to death or the emotions relating to it. In French, the translation of "Morticulturalist" is "Phytophile," which means "someone who has a passion for plants."
It could also be a portmanteau of "multiculturalist" a term used to refer to someone or something which has aspects of many cultures, referencing the fact that you are collecting many plants, and the Latin root "morti" which relates to death, and could be a reference to the fact that to get this achievement, you have to beat adventure mode, seeing almost every zombie.
The lawn ornament in the Xbox Live Arcade version is a garden gnome, with Crazy Dave's face, holding a Peashooter.
Morticulturalist is the only achievement that Crazy Dave personally acknowledges. It is also the only achievement that does not play the achievement jingle when the player gets it.