Does the HomePod control lights away from home

It can, provided there is also an active wireless connection to the Internet. Apple TV and iPads are alternatives if you are only looking for a way to enable remote control. In particular Apple TV would be significantly cheaper.

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Either HomePod or Apple TV can serve as a Home Hub to control HomeKit compatible accessories, which you should be able to control when you're away from home as long at you have an iOS device that can connect to the Internet. See iOS - Home - Apple.

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An iPad can also be used as a Home Hub but, of course, needs to stay in the house and remain connected to the house wifi. If you have one available you could use an iPad to test your setup before buying a Homepod.

I use an ATV as a hub. I sometimes take a second ATV on trips. It has not been set up as a Home Hub but uses the same AppleID. I have found that this sometimes prevents me from accessing the Home Hub remotely if my iOS device is connected to the same wifi.

It can

Create home automations with the Home app - Apple Support