I'm pretty sure your two changes will cancel each other out. Or clash terribly, or something.
Water follows the path of least resistance. It runs from high places to low ones, and generally heads towards the sea. Lakes are places where there is a depression in the ground, and water collects there for a while, either evaporating water out as more flow in, or eventually rising high enough for the water to spill over and seek lower ground again.
Your desert is 70% sand. Sand is very mobile, very fluid in its motion. Like water, it will follow the path of least resistance and tends to flow downwards. It is a serious question why, in a desert that is so very mobile, you still have depressions big enough to collect water in. I would honestly expect your desert to be generally about as flat as a pancake, since the sand would fill in as many gaps, nooks and crannies in the underlying bedrock as it possibly could - and at 70%, it can fill and smooth over a lot of variation unless your rock formations are pretty vertical. Maybe a little would pile up here or there, because of wind movement and the shelter of higher rock formations, maybe the sand layer would slant a bit as it gradually moves with the wind or towards the ocean (high to low, just like water) - but I would expect the difference to really be the top layer of sand. Maybe you can take a container of sand and use your fingers to mound and carve it, but shake it out even a bit at a time - and the sand flattens itself again and again over time.
So, your lakes? Will have to be deep. Really, really deep. Because they have to survive all the sand getting dropped in them, from wind and sandstorms and carried by your rivers and flash floods. You will be spending a fair chunk of your 30% rock to line your lakes, and raise the lip of the depressions high enough above sand level that your lakes stand a half a chance. Because I don't know of any mechanism that will get than much sand out of the depression again, to keep it a depression where water can collect instead of an under-sand rock formation. And even if each occurrence is only inches of sand - that sand will be building up storm by storm, flood by flood, by wind and rivers, year after year after year - lots and lots of sand.
Maybe they started as deep cenotes, underground caverns filled with water, and grew to shallower lakes as the caverns filled and sand competed with water for space - which would also, after a while, cut of that connection between the source of moisture and the surface. Maybe your rivers propped up the cenote-lakes, and kept them from evaporating completely, and swept some of the sand out - this would delay, not prevent, the loss of your lakes to burial under the sheer volume of sand, but maybe it's enough for you? And it would take a lot of precipitation to make your system work (make it "upstream" of your desert if you want it to remain a desert), because your rivers will have to be quite big, and carry a fair amount of water, at a rapid pace, to refill the lakes faster than the sun can evaporate them or the sand fill them. Your lakes would tend to collect sand, since the water slows there - which fills the depression in. And the force of the water still coming from the incoming river would carve a channel, and your lake is replaced by a fast moving, eroding river that can keep the sand moving with it.
Of course, if your lakes survive by sweeping the sand out with water means the sand keeps getting swept towards the sea. And sand is fluid, and like water will seek the lowest level. I expect the desert will lose sand into the sea at a relatively rapid rate - it doesn't have to wear rock down into sand, which takes a lot of time and erosion, just let the sand keep moving seaward. Sand will keep getting swept into the depression, and out along the rivers to the sea, until the lip of the rock formations is well above the sand level, and the force of water necessary will also carve deeply into the rock and erode that way, and into the sea. Water can recycle through evaporation and precipitation, but there is no getting sand (or rock) back onto higher ground. So, at the relatively rapid rate at which sand can blow and flow and deposit into the depressions and the water, it will deposit back out into the sea, sweeping a fair amount of that 70% sand out in a geologically short period of time, until there's a high enough proportion of rock again to serve as windbreaks and structural support and stuff to make the land not-flat.
It will take another fair chunk of your 30% rock to line the edges of your desert, to keep the sand from just sweeping into the ocean - and even so, I would expect your continent to be bordered by fairly shallow seas, as the loose sand keeps getting swept to sea, filling the depression, seeking the lower level, and raising the sea floor (a much larger scale version of the sand's attempt to bury your lakes). Again, it will take time for the sand to move, since it will take time for local movement to translate to movement across the whole desert - but every storm, and flood, and wind will slowly work to equalize the whole area.
So, by the end of it all, I would expect that your water system will be inundated with loose sand, and to survive run forcefully and carve deeply to sweep the sand out to sea, until there is much less loose sand and much less capacity for storing water (depressions filled flat, so no lakes, rivers erode deep to deal with water volume quickly instead). Either half the mass of sand will be lost to the ocean, making shallow seas and lots of flat shallow floodplains, and/or the volume of water needed to keep up the lakes will carve deeply into the desert, and you'll end up with deep canyons and cliffs and possibly fragment the desert (depending on the height of bedrock vs sea level vs depths of river carving). Not much like the original Sahara, unless I miss my guess.