No, there's no such thing as an "ideal switch", as that would break SPICE. That is to say, it's a mathematical impossibility in real life, and a numerical nightmare in SPICE. (You could make one using an IF() statement, but don't expect the simulation to run very well.)
The switch component more closely approximates an ideal MOSFET: the resistance varies smoothly from Ron to Roff over some range of input voltage, and therefore also hopefully over some range of time (continuity is paramount).
(Truly real switches have all sorts of nasties, from arcing and contact bounce, to tunneling, surface interfaces, and contact resistance, so aren't really reasonable to even begin to model accurately.)
Since you're adding resistance anyway, why not absorb the series resistance into the switch's Ron? The total resistance is simply the total resistance.
Also, you can accurately and implicitly solve the equation you have provided: simply connect the voltage source (RS=0) to the resistor to the inductor, and set the inductor's initial current to 0. (You may have to check the Configuration panel to make sure LTSpice doesn't override your initial condition.)
Tim