"les" is the plural form of "le, la, l'". "des" is the plural of "un, une". So to figure it out, try putting the sentence in singular: "Il y a un lac profond dans mon pays". It uses "un" in singular, so the plural must use "des".

both are undefined ''determinants'' put in front of plural words.

It is quite tricky but the hint I can give you is: if you can add ''some'' to your sentence, then the answer is DES. BUT BEWARE! it is only to give you an idea if it sounds odd or not; if the word ''some'' is part of the sentence, use the word ''quelques''

eg: The dogs were eating (Les chiens mangeaient) (Some) Dogs were eating (Des chiens mangeaient) Some dogs were eating (Quelques chiens mangeaient)

They are both undefined, but for one of them you kinda you of which I'm talking about while the other one is in general.

In english, ''There are deep lakes'' and ''There are some deep lakes'' have the same meaning, so in french ''Il y a des lacs profonds''

Few more examples...

You are eating the carrots (tu manges les carottes) You are eating (some) carrots (tu manges des carottes) You are eating some carrots (tu manges quelques carottes)

The women open the books (Les femmes ouvrent les livres) (some) Women open (some) books (Des femmes ouvrent des livres) Some women open some books (Quelques femmes ouvrent quelques livres)

Cheers