Japanese learners in particular use 'let's' grammatically correctly but unnaturally. We will first look at the correct use.
Using 'let's' correctly
First, it is the contraction of 'let us'. The 'us' means you (the speaker) and other people (2 or more).
The phrase 'let's' is used to make suggestions or offer encouragement to do an activity.
Example 1:
A: What should we do today?
B: Let's go to the park.
A: Great idea!
In this example, person B uses 'let's' to make the suggestion of going to the park.
There are two people.
Example 2:
A: What should we do today?
B: Let's go to the park.
C: Nah, I went there last weekend. Let's see that new movie instead.
A: Okay, I do want to see it.
B: Sounds good.
In this example, person B uses 'let's' to make the suggestion of going to the park. However, person C wants to see a movie so uses 'let's' to offer an alternative.
There are three people.
Alternatives
You can use 'shall we' as an alternative to 'let's'.
Using 'let's' incorrectly
Using 'let's' incorrectly comes when you directly translate Japanese to English. It is grammatically fine, but unnatural.
Example 1
This was posted on a messaging site - not directed to anyone.
Let's have a little snack
This is unnatural because there isn't the 'us'. As it was posted to a site, you can't invite people to eat the snack. A correct sentence would be:
I'm going to have a little snack.
Example 2
This was posted on a messaging site - not directed to anyone.
Let's talk to someone.
This translates as two or more people are suggesting they talk to someone. However, there is only one person writing the message. There is no 'us'. Some correct sentences would be:
I want to talk to someone.
I would like to talk to someone.
Example 3
This was posted on a messaging site - not directed to anyone.
Let's do our best for the upcoming week!
The 'us' in this sentence is the people reading the message. The writer is inviting everyone who reads it to do their best. It is a suggestion or offer of encouragement.
For me, English is a language focused on the first person (I). Naturally, English speakers do not write like this. A correct sentence would be:
I'm going to do my best for the upcoming week.
The focus is on you, the speaker.