It isnt the neem oil for certain!!, it should have killed the lady bugs
did you buy the 70% concentrate neem oil? or maybe your not using enough
as to the plants yellowing and spots .....
complete a soil runoff PH test.......
with PH corrected water (6.5-6.8PH ) pour enough water in the pots so the water runs out the bottom of the pot ...collect & test the PH of this runoff water....post both the watering going in the pots and the runoff ph
If the PH reading is out of optimum range 6.5-6.8 PH, you need to flush your plant.
Flush with PH corrected water, till in optimum PH range, 3 times the volume of the pots is the rule of thumb
but may require much more flushing if the rootball is thick & sour
EG: 1 gal pot = 3 gal. flush
add 1/2 strength PH balanced nutes to the last gallon of the flush.