I played with someone exactly like this yesterday. We're both hyperactive net players and once the other team saw they couldn't hang with our volleys, they backed up to the baseline and started lobbing like crazy.
It used to be that if I didn't get beat outright by the lob, I'd leave the court so mad and frustrated it may as well have been a loss. But one day a coach was watching and when I came off the court he told me what I should've done. I hooked up with him shortly after and he taught me some tools to use against lobsters like hitting sharp angles, drop volleys, short dribblers; shots that are hard to lob. He drilled in my head that if I hit anything beyond the service line to someone waiting at the baseline I should prepare for a hot shot to the gut but I should position myself get the lob.
He also taught me a handy formation that I used yesterday because I refused to do one up/one back like my partner suggested. Coach calls it the hot/cold seat. The person who volleys the ball (hot seat) keeps moving forward with each volley, attacking, while their partner (cold seat) holds position no more than a step or two inside the service line.
The cold seat is a guard position. It's hard to lob over that person and it puts them in position to catch a ball lobbed over the hot seat player, usually high enough to pop a volley. You can also hit effective first volleys from the position so if the opponents switch it up and start hitting to the cold seat, the roles immediately reverse. That person then hits the first volley and moves forward to attack a second. The former hot seat player drifts back and positions themselves inside the service line.
In most cases there's no discussion over who gets the lob. Usually when two people are at the net, they are side by side. Ball goes up and the person under the ball feels pressure to get it because they're closer to it than their partner. But with hot/cold, the hot seat player knows their partner is behind them specifically to cover so they're more likely to give it to them.
But some people are just stuck on stupid. If you find she still won't let you take the ball, it might be that she's just too aggressive and greedy for your styles to ever mesh.