Translation:I should eat
We would like to eat would be more like 'tunaomba kula' or 'tunataka kula' (we want to eat). 'Ni-le' is derived from the first person prefix -ni- and the subjunctive form of the verb -kula-. Monosyllabic verbs lose their -ku- prefixes and the final -a- of the vowels are changed to -e-'s. And this imperative form basically means should/must. So 'nile' basically means 'I should/must eat' = I have to eat .
IMO, "I have to eat" means "Lazima nile" or "Sharti nile" or "Sina budi (ila) kula". Just "nile" by itself means "Let me eat" (but not in the sense of allowing me to eat), or "I should eat". If it were in the form of a question "Nile?" it would mean "Shall/should I eat?", not "Do I have to eat?"
Further example: "Ngoja nile kidogo halafu tutakwenda." -- (roughly) wait let me eat a little then we'll go. There is no notion of "have to" here; one could argue there is not even a notion of "should."