My grip keeps failing on lat pulldowns

So I'm relatively new to the gym, and basically I have issues with the lat pulldown. My last session i was able to get 70 lbs for 3 sets of 12, but just yesterday, i could just get 1 set of 12 after which my grip was the limiting factor on the second set. I use lifting straps and thumbless grip, but I feel that this kinda inhibitors my ability to really work my lats.

Have any of y'all been in a similar position? Any tips? Does it get better eventually?