Hello Andrew
I found the issue with my code, it was a silly mistake on my part. For the custom fields, I wasn't including the prefix before the field name. When I fixed that, it worked fine.
FWIW, here is the code snippet:
Entity entity = new Entity("lead");
entity["lastname"] = "LastName";
entity["companyname"] = "company";
entity["new_testcustomfield"] = "customvalue";
_orgService.Create(entity);
Thank you.
Sai.