Just notary. Lic. means that the person has a licenciatura degree, in this case, of course, a law degree, but it doesn't mean the person practises as a lawyer. In other words, although lawyers are commonly referred to as Lic., Lic. doesn't always mean lawyer.

I am strongly opposed to translating "notario" as "notary public", which is very common practice. A Mexican (or indeed Spanish) notary is very different from a US notary public and to use this translation is bound to create misunderstandings. There are simply not equivalent.

The following page on "notario (público)" vs. "notary public" is relevant here; it refers to Texas, but applies to the US in general, I think. Note that when translating in Spanish, "according to Texas law the 'literal translation of the phrase ‘Notary Public’ into Spanish is prohibited'".
http://www.sos.state.tx.us/statdoc/notariopublicoarticle.sht...

You should certainly not translate "notario" as "lawyer".

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Note added at 1 day1 hr (2017-07-17 11:10:08 GMT)
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The point Sandro raises has come up before; in fact it's been extensively debated here. The issue is the one I've mentioned already: the radical difference between a US notary public, which is a common-law notary, and a Mexican notario, also referred to sometimes as a notario público, a civil-law notary. The disagreement is on what to do about it.

Here are two of the most important previous questions on the subject. It is worth reading the comments and discussions. As you can see, the clear majority view is that "notary" alone is an acceptable translation for "notario":
http://esl.proz.com/kudoz/spanish_to_english/law_general/567...
http://www.proz.com/kudoz/spanish_to_english/law_general/625...

For background, Wikipedia is pretty good on the common-law/civil-law distinction in this area:
https://en.wikipedia.org/wiki/Notary_public
https://en.wikipedia.org/wiki/Civil_law_notary

I don't think it can be denied that it is vitally important not to translate "notary public" as "notario (público)". Indeed, as mentioned above, it is illegal to do so in Texas. Unscrupulous US notaries public have been misrepresenting themselves to Spanish-speaking immigrants as "notarios": so-called "notary fraud". When translating the other way, the practical issue is less pressing, though logically you can of course argue that if it's wrong when translating into Spanish it's equally wrong when translating into English.

My own feeling up to now, and the point I've made in the past here, is that if you translate "notario" as "notary public", it will definitely create the wrong impression, but that it is acceptable to translate it simply as "notary", as most people do. "Notary public" is a term in English that refers to common-law notaries, but "notary" refers to either, and will be taken to refer to the relevant kind, which in Mexico is a civil-law notary. Sandro's position is that "notary" in US English is a synonym of "notary public" (and I have to admit that's difficult to deny), so US readers will misunderstand "notary" to mean what it means in the US.

I am still not sure it is necessary, every time we have to translate "notario" into English, to put "civil-law notary". If I am translating into British English, I wouldn't do it, largely because "notaries" barely exist in the UK so there are no preconceptions of this kind. But I must admit that given the controversy over this in the US, where the notary public is a familiar figure, when translating for a US audience there is quite a strong argument for specifying by putting civil-law notary. It can't do any harm, and it avoids any possibility of misunderstanding (if readers don't know what "civil law" means, that's their problem; they can easily look it up).

An alternative is "civilian notary" (see the previous questions), but I would not be prepared to use this. Very few people realise that "civilian" can mean this, and most will think it means non-military.