Does the pigeonhole principle rule out the possibility of losslessly simulating a universe the size of our own? Say you had a very powerful computer and wanted to run a completely lossless simulation of a universe approximately the same size as our own: $10^{80}$ particles.

Each particle in the simulation has properties like velocity, mass, charge, etc. Assuming that your program didn't use any tricks (like compressing this simulated universe by storing groups of 1000 particles as if they were one), does the pigeonhole principle mean that you would need a computer made out of at least $n$ particles to losslessly simulate a universe of $n$ particles?

I say this because I don't see how it's possible to store all of the physical properties of a particle on a piece of hardware without using at least one actual, physical particle.

Am I right about this? Does this mean it would be impossible to ever hope we could create a high resolution, lossless simulation with a number of particles similar to the actual number of particles in our universe?
No, the pigeonhole principle doesn't immediately imply that.  It might be true, but you'd need some additional reasoning to prove it.

For instance, you seem to be assuming that the way the simulation works is by separately simulating each simulated particle using one or more real particles, and that a single real particle cannot simulate more than one simulated particle. It's not obvious that either of these need to be true.  For instance, perhaps you can simulate K simulated particles using L real particles, using a complex algorithm that simulates them jointly without any clear mapping from simulated particles to real particles.  It's also not clear why we'd need to have $K \le L$; perhaps there is some algorithm where $L=K/2$ (say).  Some additional reasoning would be needed to rule out these possibilities -- the pigeonhole principle alone isn't enough.

It does seem like a plausible-ish sort of conclusion, under reasonable assumptions about your model of computation.  But I don't think it's that easy to prove.