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I have installed LimeSurvey on my laptop.
I have created a survey say trial account.
I have added a participant to this survey.
I want to send directly the survey link to this participant and record his results in a survey response.

Limesurvey need a website, an hosting.

While in theory you could run an operational Limesurvey installation from your laptop, your question indicates that you probably wouldn't be able to set this up and configure it in a secure way. You generally do not want to open the access to your laptop from the internet.

So as Denis says, you need to install Limesurvey on a webserver, e.g. you need a hosting package, a VPS or a dedicated server (or you go for the SaaS service provided by Limesurvey GmbH and others).

Limesurvey is a web application and thus needs to run on a web server that allows access from the internet. If you installed Limesurvey on your laptop, you most probably did this in some kind of test environment like XAMPP, etc. These are not made for production web applications.

Also, to automatically send emails to participants, you need a well configured email server, which you probably don't have on your laptop and don't know how to set up. Because if you would know how to do this, you wouldn't ask this questions.

So you either need some kind of web hosting to install Limesurvey on, or you need to open an account on one of the services that host Limesurvey for you.