Even if water would not be needed, you are still bound by the requirement of low viscosity and large thermal gradient, that seems to be mandatory for life as well.
Lava is just too viscous and thermal gradient is just too small on average to allow any kind of interesting conditions that would make enough interactions for life to evolve. That is, life doesnt appear, it slowly develops from life-like molecules, and it make take a long time where chemistry is not yet life, but something on the border. This pre-life evolution requires lots of generations to pass, and lava just doesnt provide enough generations for this to happen.
Carbon is way more common than phosphorus, and provides stronger bonds too. If you want your life not to use carbon, you need it to give a convincing reason not to. One way is to just to make sure there is about 1000 times less carbon than there is now. There is no way a planet formation would provide this difference, neither smaller nor bigger planet will change this much, nor will stronger solar wind be able to strip carbon but leave oxygen with ratio that is sufficient.
One way provide conditions where carbon is this rare is to change the fusion process in stars. Currently fusion process doesnt make much lithium, berillium, boron. Carbon is just after them. If fusion process is changed so that carbon is as unlikely to form or remain stable as those elements, then you will have sufficiently rare carbon to justify the use of phosphorus.
Early universe will not work for your scenario either, carbon forms before heavier elements do.
Carbon-based life that has eaten all the carbon but then stopped its evolution is also extremely unlikely. As just a few evolving cells will continue the evolution of carbon based life, and even early carbon based life is likely to eat all the materials that other life could need.
Artificial life is always an option. If sterile planet is inseminated with a ready non-organic life, organic life will not have enough time to emerge.
Just accident is also always an option. Given large enough universe at some point non-carbon life will win just by accident. Even if odds are many orders of magnitude worse.
One way that might have some sort of chance is an alkaline planet, that has no volcanic activity. This way no CO2 is emitted by volcanoes. And CO2 that is present is absorbed by the alkali metals. For this to work planet must suffer from a large scale erosion, that would grind up the rocks, to make them absorb CO2. And you still need lots of thermal gradients for life to kickstart. Very rapid planet rotation could probably provide enough thermal gradient to substitute lack of volcanic based hot sources that we have. Very rapid rotation would also likely make extremely strong wind, that will help with the erosion, that would help to absorb CO2 into rocks. It would also even out the planet's surface, removing mountains and deep seas. If amount of water is just right, a few meters or so, then the whole surface of the planet might work as an evolution chamber for the pre-life. Unlike just a few hotspots that we have. This could somewhat balance out the chances for weaker links in the chemistry you propose. To make sure volcanoes dont work, planet needs to be colder than ours, and not be close to any large body. So it cant be a moon or be next to a small star, otherwise gravity will heat the planet up. So it must be a small planet, located near a big star. But it also must be not a water world. So it must get its material from the inner region of the star system, or solar wind must be strong enough to blow away most of the water. Material from the inner region is preferred. If strong solar wind has blowed away 99% of the water, then planet wont have long before there is no water left. Material from the inner region that has migrated outside is also not that stable, comets fom the outer region will keep adding water, and sea may become too deep eventually. But something on the border of this two options might just work.