Lightspeed eCom supports the MailChimp app. This integration allows you to automatically export your store's newsletter subscribers to your MailChimp mailing list.
To purchase the app, go to Apps > App Store in the left menu of the Back Office.
If you prefer to manually import your newsletter subscribers into your MailChimp mailing list, go to Tools > Exports in the left menu of the Back Office; then, click New Export and select Newsletter Subscribers from the drop-down. You can then import the exported file into MailChimp.