The emails is not dependent upon WPLMS, WPLMS uses wp_mail (wordpress mail) function for sending emails. Activation emails are sent by BuddyPress.
It is mostly a server related issue.
Following pointers will help you in resolving this :
a. Try contacting your web-host.
b. Ask your customer to check the spam section as well.
c. Try installing
WP Mandrill plugin, it provides an external SMTP server for all your emails, upto 2000 emails free/month. If the issue gets resolved with this, it confirms that the issue lies in your server.
Quick fix :
All the users registering in your site go into pending submissions area. Located in WP Admin - Users - Pending submissions, you can re-send the activation email to them to directly activate the user from there.