DNS does not resolve with NGINX in Kubernetes

Resolving the name fails because you need to use the Full Qualified Domain name. That is, you should use:

lead-api.<namespace>.svc.cluster.local

not just

lead-api

Using just the hostname will usually work because in kubernetes the resolv.conf is configured with search domains so that you don't usually need to provide a service's FQDN. e.g:

search default.svc.cluster.local svc.cluster.local cluster.localnameserver 10.3.240.10options ndots:5

However, specifying the FQDN is necessary when you tell nginx to use a custom resolver because it does not get the benefit of these domain search specs.

You need to use a Service

http://kubernetes.io/docs/user-guide/services/

A kubernetes Service proxies traffic to your Pods (i.e. what you call 'service', which is your application)

I guess you use Kubernetes for the ability to deploy and scale your applications (Pods) so traffic will need to be load balanced to them once you scale and you have multiple Pods to talk to. This is what a Service does.

A Service has its own IP address. As long as the Service exists, a Nginx Pod referencing this Service in upstream will work fine.

Nginx (free version) dies when it can't resolve the upstream, but if the Service is defined, it has its own IP and it gets resolved.

If the Pods behind the Service are not running, Nginx will not see that, and will try to forward the traffic but will return a 502 (bad gateway)

So, just defined the Service and then bring up your Pods with the proper label so the Service will pick them up. You can delete, scale, replace those Pods without affecting the Nginx Pod. As long as there is at least one Pod running behind the Service, Nginx will always be able to connect to your API.