You can install LASR on the new computer using the same download link and license key as you did originally and follow the on-screen instructions for moving your license.
Your plugins are permanently tied to the license and will transfer with your license.
If you cannot find your download link and license key:
On the new computer, LASR Will show you a prompt saying,
"There was a problem with your license. No License was found. Please add a valid license."
Click the OK button on that message box.
Enter your license key into the "License Key:" text box and click the "OK" button.
You will be prompted with the following screen:
Agree to the terms by checking the "I Understand" checkboxes and clicking OK. After that, this shows:
Check the email listed on the dialog box, and click the button in the email that gets sent to you:
After clicking the "Confirm Moving LASR License" button in the email, go back to LASR and click the OK button:
Fill out the form (first & last names, email address, etc.) and click the OK button:
You have now moved your license to your new computer.