Let’s is the English cohortative word, meaning “let us” in an exhortation of the group including the speaker to do something. Lets is the third person singular present tense form of the verb let meaning to permit or allow. In the questioner’s examples, the sentence means to say “Product (allows/permits you to) do something awesome”, so the form with lets is correct.
I find the distinction that MacMillan makes between not to mention and the supposedly synonymous let alone and still/much/even less useful: The phrases let alone and still/much/even less reinforce a negative or unlikely statement that precedes them. The still/much/even less constructs reinforce the negativity of the preceding phrase by subtraction -- Negative statement, still/much/even less ...
Not to Mention ≈ [Let Alone ≈ Much Less ≈ Still Less]
Bay Area Reporter: Fangs, but no thanks: 'Let the Right One In' at Berkeley Rep
Fangs, but no thanks: 'Let the Right One In' at Berkeley Rep
Deadline.com: ‘Adolescence’ Writer Jack Thorne’s UK Tour Of ‘Let The Right One In’ Play Cancelled
The UK tour of the play Let The Right One In, penned by Jack Thorne, has been cancelled due to “unforeseen circumstances.” BBC News reports that the production, based on the best-selling Swedish novel ...
‘Adolescence’ Writer Jack Thorne’s UK Tour Of ‘Let The Right One In’ Play Cancelled
The touring production of Let The Right One In has been cancelled. Based on the best-selling vampire novel and film by Jon Ajvide Lindqvist, it is adapted for the stage by Jack Thorne, who co-wrote ...
Performed fittingly on Halloween, this stage version of Let the Right One In adapted from John Ajvide Lindqvist’s novel and film captures the eerie chill of Blackeberg, Sweden. The story follows Oskar ...