First of all your statement:
In English, the lemma of a verb is the 3rd person singular form
is incorrect. The 3rd person singular of an English verb would be "he asks", "he
digs" and "he is". Id don't know any dictionary to use this form. So, it probable the infinitive rather than the 3rd person singular although in English it's hard to guess sometimes. See wikipedia article also:
In English it usually is the full infinitive (to go) although
alphabetized without 'to' (go)
All person except the 3rd person singular coincide usually with the infinitive, with possible exception the verb "to be":
Anyway, to your question now the same link of Wikipedia just answers your question but I guess you validated the answer as complete enough:
In morphology and lexicography, a lemma (plural lemmas or lemmata) is
the canonical form, dictionary form, or citation form of a set of
In other words it says that lemma is the
- canonical form meaning the form of word that is standardized, deprived of most conjugation ending and transformation and meant to be an anchor for all searches involving all forms this word might appear.
- dictionary form just means it's the form you look up in a dictionary for the above reason (easier to search for)
- citation falls into the same category as the dictionary form: easier to cite.
The second part of your question which you express your doubts about the inconsistencies of the criteria to give lemma status to a word, is exactly that.
- at some point the original lemma cannot deal exactly with the intend it was used initially, meaning to be searched easily. So, then lexicographer often add new entries which seems to break the lemma contract but they stick to the general rule of a standardized way to search a word.
- This explains also cases, where multiple lemmas seem to address the same (morphologically) word. Then, there might be a shift in which part of speech the two words belong to, e.g. verb vs noun etc.
How is it scientifically defined?
I don't think there is a large science behind it, it's just a convention that is used to refer to words and search them easily. It's like asking why the words are look up in this alphabetical order and not another order, e.g. by phonology etc?