We have examples for PHP, C#, and VB.NET showing how to call the LimeLM function limelm.pkey.generate and then parse the response to get the product key. You can see the exact code by downloading the LimeLM Web API Pack and looking at the code inside PaymentSettings.cs (for C#), PaymentSettings.vb (for VB.NET), or PaymentSettings.php (for PHP).
We don't have an example specific to Cleverbridge, but we can help you write it if you need one. Also, if you're not using PHP, C#, or VB.NET we can help you write it for whatever language you are using. Does Cleverbridge run code that you post, or do they call external URLs an parse the response?