Yes, but the lifetime between charges may be quicker than you think. Normally a 9 volt battery has 6 each 1.5 volt batteries in series. But Li-Ion batteries put out 3.3 volts or so. A 9 volt lithium battery may actually put out 10 volts on a full charge, but the 3 tiny cells in series are no better than a good alkaline battery.
The Fluke 87 III is miserly with its power consumption and has a sleep mode for the display if you have it in record mode.
Initially the rechargeable lithium batteries may seem like a good buy, but remember that if one cell goes bad from overcharging or from letting them go dead, it will block any current from the good cells, so it may seem that in the long run you have to replace them more often than you thought.
I have used 9 volt lithium batteries before and was disappointed at their maximum life-span, so we went back to using good alkaline batteries, which last a full year but are replaced every year by UL testing standards.