what it means to say maxwell's equations have 'predictive power' is that we can
1. take a situation observed or designed in the contingent universe,
2. translate it into the abstract entities maxwell's equations talk about,
3. deduce consequences in the world of abstract entities,
4. translate those consequences back into the contingent universe, and then
5. find that the consequences in the contingent universe are within narrow uncertainty bounds we translated from the abstract world of ideas
the meaning of turing universality is precisely that any turing-complete programmable system can be used to model any other logical or mathematical system, including other turing-complete systems, in exactly the same way that maxwell's equations model electromagnetism
for example, you can model risc-v execution in lisp and predict what a risc-v processor will do, you can model lisp execution in the λ-calculus and predict what a lisp interpreter will do, you can model the λ-calculus in a turing machine and predict what λ-reduction will do, and you can model a turing machine in a risc-v processor and predict what the turing machine will do
there is a significant sense in which this sort of modeling is much more perfect than the kind done with maxwell's equations
when we apply maxwell's equations, we are subject to measurement error in steps 1 and 5; our measurements are never complete and correct, and heisenberg's uncertainty principle strongly suggests that they never can be. and in step 3, because maxwell's equations are continuous-time continuous-space differential equations, we often also introduce numerical error in our calculations as well, because we usually have to integrate them numerically rather than algebraically
on the other hand, in the case of computational universality all the entities being discussed are discrete, algebraic, mathematically abstract entities, so our simulations are absolutely perfect unless we run out of memory or suffer a rare hardware error
obviously these universal machines are not limited to modeling other universal machines; we can also use lisp or turing machines or risc-v processors to model things like gravitation, taxation, or maxwell's equations. and they are obviously also the main working tool for all electrical engineers today, having displaced slide rules and load lines generations ago
ultimately, though, we are also using maxwell's equations (and other equations describing electromagnetism, like the ebers-moll transistor model) to design our electronic computers which we use to simulate lisp
I think you're confused about the premise of this discussion. The comparison is not between Maxwell's equations and lambda calculus, it's between lambda calculus and other theoretical constructs in CS.
Maxwell's equations are "the Maxwell's equations" of physics because they are "the most successful" physical theory: i.e., incredible accuracy, wide applicability, and concision. This is relative to other physical theories. (I guess you could debate whether this is actually the case---obviously this is all subjective, and not everyone agrees. Maybe someone thinks Einstein's field equations should really be "the Maxwell's equations" of physics.)
To say that the lambda calculus or anything else are "the Maxwell's equations" of computer science is to say that they have the same set of properties relative to other let's theoretical constructs in computer science. But is this actually the case? It seems like Turing machines, lambda calculus, etc. are all similar in terms of relative modeling utility and concision. I disagree that they are widely applicable---in practice, just about any commonly used programming language is far more widely applicable than anything of these. And as you pointed out, by Turing universality, they're all logically equivalent---so the question of difference in modeling "power" is not relevant here.
I guess I just don't think it makes much sense to talk about anything in CS being "the Maxwell's equations" of CS. In physics, a wide variety of disparate physical phenomena are being modeled, with individual models having a quite varied range of power and applicability. In CS, things are much different.
Incidentally, even if you simulate Maxwell's equations on a computer using Lisp, a Turing machine, or whatever else, you will not go far if you insist on algebraically exact computations. :-) As you say yourself, you must integrate them numerically, which means numerical error introduced through your discretization. But I honestly can't say I understand your point including this information above.
there are lots of equivalent formulations of maxwell's equations (cf. https://en.wikipedia.org/wiki/Mathematical_descriptions_of_t... for a few); the ∇× ∇· one we most commonly use is quite a bit more compact and usable than maxwell's own formulation because vector calculus was, to a significant degree, invented to systematize maxwell's equations. there's apparently an even more compact form of them in terms of clifford algebras that i don't understand yet, \left(\frac{1}{c} \dfrac{\partial}{\partial t} + \boldsymbol\nabla \right) \mathbf F = \mu_0 c (c \rho - \mathbf J).
similarly there are lots of equivalent formulations of universal computation. lisp and the λ-calculus are analogous to the geometric-algebra formulation above and the more commonly used form in terms of vector field derivatives: they look very different, and they make different problems easy, but ultimately they all model the same thing, just like the various formulations of maxwell's equations
maxwell's equations are the maxwell's equations of classical electrodynamics, not of physics. without a lot of extra assumptions they won't get you very far in understanding why solid things are solid (which depends on the pauli exclusion principle) or why some nuclei break down or how transistors work or how stars can burn or why mercury's orbit precesses or why hot things go from red to orange to yellow when you heat them further
my point about modeling maxwell's equations in lisp (etc.) is that lisp (etc.) can model maxwell's equations (at least, as well as any other effective means of calculation we know of can model them — discretization and rounding error also happen when you numerically integrate with pencil and paper), so if we're looking for incredible accuracy, wide applicability, and concision, lisp (etc.) would seem to trump maxwell's equations — but good luck trying to build a computer without electromagnetism, maybe you can in some sense do it on a neutron star but not with atoms