Yes. Liability coverage attaches to the registered vehicle, so a lapse or an uninsured citation can reach the registration as well as the driving privilege. Clearing it means proving coverage, not just paying a fine.
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This catches households harder than a license action in some ways, because a suspended registration parks the vehicle regardless of who is driving. In a two-vehicle household in Papillion or La Vista where both cars are working vehicles, that is an immediate problem for people who did nothing wrong. The practical sequence is to get coverage in force on that specific vehicle, then work the state notice to clear the hold, and to check every titled vehicle in the household rather than only the one that was cited. Dormant vehicles are a common source of quiet lapses: a second car that sits between uses, a policy cancelled when a payment failed, and nobody notices until the registration comes up.