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CAn I say,

(a) We enjoyed lunch together.

(b) We enjoyed eating / having lunch.

(c) We enjoyed the lunch.
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Vincent TeoCAn I say,

(a) We enjoyed lunch together.

(b) We enjoyed eating / having lunch.

(c) We enjoyed the lunch.
They are all grammatically correct.
Comments  
Vincent TeoCAn I say,

(a) We enjoyed lunch together.

(b) We enjoyed eating / having lunch.

(c) We enjoyed the lunch.

Note, that in letter b and c, it is not abolutely clear, that you had lunch together with the children. of course, it depends on the previous sentence, which might make this very clear.

ch[H]eers