With the exception of Lois, no one else seemed to have an issue with allowing WW to use her lasso on them. Obviously, up until that point, none of them had shared anything with the people holding them. Diana's presence, IMO, made all the difference. They felt safe and protected with her there, in a way they didn't before she arrived. So they agreed to do what needed doing to, not ensure their freedom, but to increase the likelihood of not being bothered by the government again. Either way, it was clear Diana wasn't leaving without the hostages. The lasso had a greater long term solution than simply getting them away from the facility, which was a very short term plan.
And Clark's sudden issue with Diana's use of her lasso, especially when Tomasi just wrote her using it in a sneaky fashion in the Circe arc, is a bit much. This is even more true since it was Clark who, if I'm not mistaken, came up with the plan. He at least agreed with it. At that point, Wonderstar had done nothing but "help" the couple. But Clark had no problem with Diana tricking Wonderstar so Diana could read the truth from him, which isn't how the lasso worked in the past. That is another Tomasi spin on things that adds nothing to the character of WW.