Just bought a few of the light strips. Since these devices have to be powered via a wall outlet, do they repeat the z wave signal, or do I need to buy some repeaters to extend my z wave network?
Yes, LZW45’s do act as repeaters.
They are Z Wave Plus and act as repeaters. Now, if your Z Wave network isn’t strong (meaning your hub is in the basement and your other devices are on the 4th story of your mansion), then you may need to stick some repeaters in between.
That’s great news! I wasn’t sure because I didn’t see it listed anywhere in the manual. Thanks for the help!
My mansion is only 3 stories, but close enough! 
Thanks for the help!
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As a rule of thumb, devices powered via wall power (vs battery) are repeaters.