The lasso might mess with his soul unless Juggernaut has shown that his soul is incredibly fortified from such direct manipulation or he has no soul period.
No. A lot of zealous WW fans will tell you that it is, and others will argue the lasso isn't that potent to begin with.
It's really in the middle ground, all things considered. It depends on what effect she's going with. There's the basic truth aspect, the ability to peer into someone's soul and gain knowledge/insight from it, using it primarily to restrict someone, offensively using the fires of Hestia to sear someone's soul, outright soul ravaging, or using it to cancel/ward off spells.
People without souls have resisted it as there is nothing for Diana to see into. A sufficient reality warper like QoF, especially as her power is effectively plot device, can actually mess with the lasso itself.
Generally speaking, based on who it has effected, the issue isn't if the lasso would work, but if Diana will:
A.) Successfully ensnare them with it to begin with.
B.) Even resort to the lasso to begin with.
C.) Use a specific ability of the lasso if she does use it and catches them.