Question: Is there easy way to get notified on change in dynamic IP address without running a local server? 

I'm aware that similar questions have been asked, but those questions and answers to them predicate a "server" being run and using a dynamic DNS service. I don't run a server on my machine and have no intention to. So if you are not running a server and thus you don't have a domain name, can you still get notified of change in your dynamic IP address, via email or whatever?

Answer: 
You can still use a service like no-ip.com or dyndns.org to keep track of your external IP even if you don't have anything running to connect to. You'd need the service's dynamic update client running somewhere on your network, still, though. You don't need to run the dynamic client on a server, just on any system that will be up a decent amount of time.

Then, an `nslookup {a host name you pick}.no-ip.com` or similar from a Windows, Linux, or Mac OSX command prompt would tell you, without requiring you connect to your home network at all.

If you use Gmail regularly, and mostly on your home network, you can log into your email from an outside location, click on the settings icon, scroll all the way down to the lower right where it says "Last account activity" and click on "Details." A list of recent IPs that accessed your account can be found and you can find your home IP that way.

You can, of course, write your own script that checks your IP periodically and does something, such as send an email, when it changes.

There is no way to tell your dynamic IP from outside of your network without something inside of your network communicating that to a point outside of your network. Your ISP is usually not obligated to tell you this and likely won't willingly.
If you use PFSense (An Open source firewall), it has the DynamicDNS settings and also SMTP setup to email you whenever the ip address changes.