First things first:
A titanium [dentist's patient] apron would weigh about 6.6 times a lead apron.
This is true in their specific example, because the mass attenuation coefficient of lead is about 6.6 times higher than titanium for 60 keV x-rays. Crank the x-ray source up to 10 MeV and lead is more like 1.82x more effective than titanium, and substantially less structurally sound.
As a secondary benefit, materials that are more transparent to low-energy x-rays are more amenable to inspection via x-ray cameras after assembly, which will help with quality control somewhat.
Now onto the meat of the question. Most of the critical points were mentioned in comments above, but I'll aggregate them here:
The most important forms of radiation that spacecraft near Jupiter will be afflicted with are charged particles trapped in Jupiter's prodigious magnetic field... captured electrons and protons and some alpha particles from the solar wind, but also heavier ions produced from other sources like sulphur dioxide escaping Io. There aren't actually any serious x-ray sources out there at all that you'd need to protect a spacecraft from.
It turns out that lead is actually a worse shielding material than titanium is against electrons with a kinetic energy ⪅10MeV, and only slightly better against higher energy electrons. Here's a chart showing the Continuous slowing down approximation range for electrons in lead and titanium, using values taken from the ESTAR database. Higher y-axis values imply more shielding is required.
Here's a chart showing CSDA for protons in lead and titanium, with data taken from the PSTAR database. You can see in this one that lead is slightly worse at any energy.
There's also a secondary problem in the form of what happens to the kinetic energy of the charged particle. The faster you slow a particle down, the higher energy the resulting bremmstrahlung x-rays have. The peak energy release will occur at the end of the particle's track through the shielding. This means that dense lead shielding that is just thick enough will produce high-energy x-rays from the inside face of the shielding. Less dense shielding (like titanium) will produce much lower energy x-rays which are more easily absorbed by the remainder of the shield and less destructive to the shielded objects.
Finally, you're left with then are a bunch of structural compromises, like how strong your shielding needs to be, and how thick it needs to be (lightweight composite shielding is great, but quite bulky, for example) and financial compromises, like the cost of obtaining and machining huge chunks of titanium, or the additional time and money required to fabricate multi-layer shielding.
The Europa Clipper project has (I believe) a radiation vault made of aluminium as well as titanium in order to keep cost and weight down (they had to knock a couple of billion dollars off the ticket price of the Jupiter Europa Explorer somehow), and I've found a paper on its shielding (paywalled, and I'm not coughing up 30 bucks to read it) which also suggests the use of tantalum sheets as secondary shielding to be used on sensitive components inside the vault to make up for the less effective vault.
In any case, no-one seems to want to use lead for any kind of shielding. Great for x-ray aprons, a bit rubbish for spacecraft.