Hi, Penn State has a useful spotted lanternfly (SLF) website with current best management practices. It is regularly updated, as research is ongoing.
SLF have been shown to kill tree-of-heaven (ToH) and grapevines, but no other plants or trees. They are known as plant-stressors, which is obviously not a good thing, but they haven't been shown to kill fig trees.
As for SLF biology - at all life stages (other than while in the egg masses) they require food, and have a piercing mouthpart that relies on the turgor pressure of the plant to push the fluid from the stems/branches into the SLF in order to feed. So, setting out soap/water/sugar mixtures will not attract nor kill them (unless they fall in and drown!) because they cannot feed on it. I've attached a PDF of their lifecycle (one per year) for your reference. This year I saw my first adult on July 1st, but there are plenty of 4th instar nymphs out there still too.
There are directions for homemade circle traps available here and a good video here, and there are premade ones you can purchase from Great Lakes IPM. If you choose to use sticky tape, then it is highly recommended that you use a wildlife barrier to prevent bycatch. It is advised NOT to use homemade pesticides for SLF nor for pretty much every other pest issue. Just because something is safe for one purpose, doesn't mean it is safe for another purpose. Soap, salt, and other household items can have unintended consequences on non-target species, plants, soil, water, etc., when used not as intended. See here and here for more information.
Getting rid of the ToH would be useful in this battle, but that too can be tricky and DOES require a specific protocol and the use of an herbicide.
In my own garden, I use an empty vitamin water bottle to catch them. If you hold the opening in front and slightly above them, they will likely jump right into the bottle (see attached photo). You can shake it and dump it out and then smash them, or put the bottle in the freezer, or dump the contents into a container of soapy water or rubbing alcohol to kill them.
If you have any questions, you can also call the Philadelphia Co. Cooperative Extension office at 215-471-2200 and select the Master Gardener hotline for assistance.