lets or let's

[new2grammar]

Let's strike a conversation

or

Lets strike a conversation

Regards,
Jasmeet Singh

 

[5jj]

Let's strike up a conversation.

This strikes me as a rather unnatural utterance.

 

[Rover_KE]

Note that let's here means let us. The apostrophe replaces the missing u.

'He lets me drive' = 'he allows me to drive'. Nothing is missing from lets.

Rover

 

[JMurray]

Let's strike up a conversation.

As 5jj says, this doesn't sound natural by itself if it is one person asking to converse with the other. A native speaker is more likely to say something like "let's talk", "let's have a chat" or just start talking.
But this is ok: We had never been to this town before but my friend said, "Let's strike up a conversation with the first person we meet".

not a teacher