Lowrider Hydraulics

Other than the added weight, are there any performance losses related to installing 'lowrider' hydraulics?

Not direct performance reductions, but to my knowledge there are some related problems.
Often the low riders I see use skinny undersized tires, partly to make the car seem lower and partly to provide better wheel well clearance during various suspension gyrations. Such tires will not help traction or cornering, but are not essential to the low rider equipment list.

All the low riders I have seen have no sway bars - again, to assist the suspension gyrations. Of course, enthusiastic cornering will suffer, unless the suspension is flopped all the way down. But, if you drive like that, the car will bounce over bumps, which can disrupt enthusiastic cornering.
Of course, unless you want to build a car that can lift one wheel like a dog lifting a leg at a fire hydrant, you can leave the sway bars on.

IMHO unless you want to build a car specifically for hopping, use an air spring system. It will give you most of the ride height versatility of hydraulics with better handing and ride and much less weight.

^^^ ditto