Uneducated opinion here however at this point I have enough experience losing and gaining money in spreading NG and CL that maybe it's possible to give some thought to it.
CL has a lot of hard problems. It's hard to store, kind of expensive to process, and dependent on season consumption in the form of travel/boats/aircraft/etc. The coronavirus has chopped out nearly every form of consumption possible and, given that oil producers begin storing in January or so, there's a massive glut of oil that is not going to be spent. Moreover, you can't just "stop" crude oil production with a single switch. Moreover again, it's fairly expensive per barrel to make refining make sense in North America.
NG doesn't have many of these problems. I'd even argue they aren't very correlated. NG can be stored in a ton of different places - pumped into salt mines, containers, etc. It can be burned off if needed since NG is relatively clean burning. Consumption is fairly regular even given a pandemic since people need to heat and cool their homes.
I think it would be unlikely for NG to do what CL is doing. CLs behavior is a function of just how hard it is to store and just how important consumption is.