Theoretical LENR device would be comparable to an RTG [1] because at high heat the device would melt itself. It's more about a trickle of stable power, rather than being used as a cell of a power plant. So, ignoring support infrastructure and focusing on the size of the power generator, we have:
Using the power source for the voyager probe as an example:
RTG size: 0.5m x 0.5m x 1m == 0.25 cubic meters.
RTG power: 2400 watts (thermal)
RTG power density: 9600 watts per cubic meter
Using ITER as an example for the scale of fusion power plant:
Reactor size: 800 cubic meters
Reactor power: 500,000,000 watts (thermal)
Reactor power density: 625,000 watts per cubic meter
So yeah, theoretically it would be compact, but low power density. Enough to power a space probe, but not our civilization.
[1] https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_ge...
If it is not that compact but it can still be placed inside homes, ditto.
How do you come to that conclusion?
The RTGs that powered the voyager probes output 470 watts. That is about 7 lightbulbs.
A Tesla Model S uses up to 345,000 watts (463 hp)