The downside to using a 9 volt battery is the low output; in other words, they don't last very long. They have about the same amp hours as 6 AAA [hooked in series to make 9 volts]. AA batteries last about 2.5 times, c-batteries last about 4 times, etc.
Hooking batteries in parallel will more than double the run time. Other factors besides the load affect battery life especially internal battery heat caused by high drain loads.
My lighted lithophanes have a dual power source, 9-volt battery or a 9-volt DC adapter [REALLY CHEAP ON EBAY]. The 9-volt battery will only last a couple of days.
The led's should have the power consumption listed somewhere on the label. You will find different descriptions on the labels from different manufactures; Power = Volts x amps = watts = volt-amps
Ampere-hours = the number of hours the battery will last at the given amp load.
Hope this adds to the help already posted.
You will get old if you live long enough!