Introduction:
The encysted stage refers to a stage in the life cycle of certain parasites when they form a protective cyst around themselves. This cyst helps them survive in unfavorable conditions such as when there is no host available or when the environment becomes harsh. In this question, we are asked to identify the organism for which an encysted stage does not occur in its lifecycle.

Entamoeba gingivalis:
Entamoeba gingivalis is a protozoan parasite that inhabits the oral cavity of humans. It is commonly found in the gingival crevices and between the teeth. Unlike other species of Entamoeba, such as Entamoeba histolytica and Entamoeba coli, Entamoeba gingivalis does not have an encysted stage in its lifecycle.

Entamoeba histolytica:
Entamoeba histolytica is a parasitic amoeba that infects the intestines of humans and other primates. It has a complex life cycle that involves two stages: a cyst stage and a trophozoite stage. The cyst stage is the infective stage, which allows the parasite to survive outside the host and be transmitted to a new host. The trophozoite stage is the active stage, during which the parasite feeds on the host's tissues and causes disease.

Entamoeba coli:
Entamoeba coli is another species of amoeba that can infect the intestines of humans. It also has a life cycle that involves a cyst stage and a trophozoite stage. The cyst stage is resistant to environmental conditions and can survive outside the host. When the cyst is ingested by a new host, it transforms into a trophozoite, which then multiplies and causes infection.

Amoeba:
Amoeba is a genus of single-celled organisms that belong to the phylum Amoebozoa. These organisms have a simple life cycle that does not involve an encysted stage. They exist as trophozoites, which are the active feeding stage, and they reproduce through a process called binary fission.

Conclusion:
In conclusion, the encysted stage does not occur in the lifecycle of Entamoeba gingivalis. This stage is present in other species of Entamoeba, such as Entamoeba histolytica and Entamoeba coli, as well as in other amoebas. The encysted stage allows these parasites to survive in unfavorable conditions and facilitates transmission to new hosts.