In general, lacto-ovo vegetarians (LOV) whose diets are not supplemented with B12 have lower serum B12 levels and higher homocysteine levels than non-vegetarians—see Homocysteine and Mild B12 Deficiency in Vegans.
Though B12 is less of a concern for LOV than vegans, if B12 supplements or fortified foods are available, they should be used regularly to ensure optimal B12 status.
A 2017 study of mainly Hindu lacto-vegetarians from Pakistan, who didn’t consume much dairy, found that about half of the vegetarians had B12 deficiency (1). Of the 100 vegetarians, 44% had elevated methylmalonic acid levels indicating a functional B12 deficiency. The frequency of depression was 31% compared with 12% in the omnivores (p=0.002), paresthesias was 11% compared with 3% in the omnivores (p=0.04), peripheral neuropathy was 9% compared with 2% in the omnivores (p=0.05), and psychosis was found in 11% subjects compared with 3% in the omnivores (p=0.04).