Final answer:
The likely consequence for a eukaryote lacking telomerase is the reduction in chromosome length in gametes. Telomerase normally maintains telomere length during cell division, and without it, critical shortening of telomeres occurs, leading to cell aging and death.
Step-by-step explanation:
A eukaryote lacking telomerase would most likely experience a reduction in chromosome length in gametes, which is option B. Telomerase is an enzyme that adds repetitive nucleotide sequences to the ends of chromosomes, known as telomeres, which prevents them from shortening during cell division. In the absence of telomerase, with each cell division, telomeres become progressively shorter until they reach a critically short length, leading to cell aging and death, rather than becoming cancerous. This is particularly crucial in gametes, which contribute to the next generation, as the progressive shortening can eventual result in fertility issues or genetic abnormalities in the offsprings.