How do you connect your LeadPages to ClickDimensions is actually a question of how do you connect LeadPages to Dynamics CRM. As of today 3/17/16 there is no easy way to do this.
The best way to approach this is to simply have your LeadPages account email you when someone fills out a form. The goal of a landing page is to convert a visitor into a lead. You can still accomplish that task even without an integration. Concentrate on getting step one done which is generating the lead. Yes, there will be a little extra work for now but that is the only way to approach this.
Direct Integration Tools: LeadPages to ClickDimensions
There are currently a few open projects on Zapier where you can vote for these integrations:
You can vote for this integration here: https://zapier.com/zapbook/leadpages/microsoft-dynamics/
There is another integration that is pending from Zapier which is the Gravity Forms to Dynamics CRM Integration. You can vote for that here: https://zapier.com/zapbook/gravity-forms/leadpages/. Gravity Forms does have an addon for Dynamics CRM: https://codecanyon.net/item/gravity-forms-crm-addon/10521695.
We will keep an eye out for any updates on this.