I believe 'The lake is here.' would correspond to 'Озеро здесь.' or 'Озеро тут.'
'Вот' is not really an adverb 'here', it's the word you use when you point to something and want to draw attention to it. The closest thing English has is 'Here is...', but please keep in mind that 'вот' is not really 'here'.
In my experience as a native English speaker, "there" is almost always used when pointing at something no matter how close. "Here" is used when touching something, when handing something to somebody, or when noting something that appears, no matter how far away, without pointing at it. Therefore, whether вот is translated as "there" or "here" would depend on the situation.
Pointing across the table, "There is your fork." Вот твоя вилка.
Handing your book to you, "Here is your book." Вот твоя книга.
The moon suddenly appears from behind a large thick cloud, "Here is the moon!" Вот луна!
In my experience with Russian, there are uses of вот that involve a figurative "pointing":
to introduce an explanation, "Here's what. ..." Вот что. ...
to conclude an explanation, "... That's it." ... Вот что.
There is also a well-known song by Vysotsky, "Вот это да". https://www.youtube.com/watch?v=kv1SBYUcbq8
You can find many suggested translations by entering the three words in the search box at http://www.multitran.ru
Here are just a few from that site: How about that; hubba bubba; sakes alive; that takes the cake; good grief; holy Moses; my word; strike me pink; my oath; dash it all; crazy; hot dog; blow me down; oh my hat; son of a gun; I'll be a monkey's uncle; fancy that.
That's strange! They should be distinguished by the stress, the singular is о́зеро /'ozʲɪrə/, the plural is озёра /ɐ'zʲorə/.
Is it possible to use a definite article in "there is..." construction?
"There is a lake" - "Есть одно озеро". NOTE! There are rare cases in Russian when "the article" is required. (even though they tell us Russian does not have any). To me the sentence "Есть озеро" does not sound natural. "Есть одно озеро" is much better.
While I agree that these sentences are interchangeable in many contexts, there are situations in which you would prefer to use the one rather than the other. When you set out to show a specific item to a person, you are probably more inclined to use a phrase such as '(Look,) Here is the lake.' Similarly, Вот озеро is indicative in nature, and it is natural to use it whilst pointing at things.
The sentence 'The lake is here' is slightly less emphatic (even in English, I guess), and you can use it when mentioning something in passing ('By the way, the lake is here.') or when pointing to several things in sequence. The Russian sentences used in such a context would be Озеро здесь and Озеро тут, respectively.
In Italian and French (and probably other Romance languages, too), you can actually find a similar distinction between the emphatic phrases (It.) 'Ecco il lago.', (Fr.) 'Voici le lac' and the more neutral phrases (It.) 'Il lago è qui/qua.', (Fr.) 'Le lac est ici.' And in the Vulgate Bible, the famous words used by Pontius Pilate when presenting the scourged Christ are 'Ecce homo', which - literally translated into Russian - would be Вот человек. There is probably no elegant and unambiguous way to translate such sentences into English: 'Behold the lake.', for instance, sounds dated (if not archaic) and gives you a wrong impression of the grammatical structure of the original language.