Your real circuit will have inductive and capacitive coupling, as well as resistive loss along conductors (especially ground traces), all of which contribute to its behaviour, and none of which are usually modelled. Also, passives like R, L, C are all ideal by default in LTSpice, but not in the real world. You need to add the parasitics in to them if you want more realistic modelling. Add ESR and ESL to Caps, add Cp and ESR to inductors. You might add series inductance to resistors (ironically, the easiest way is to use an inductor in place of the resistor). I sometimes find that regulators don't like ideal capacitors on the output, and I need to add realistic ESR to get stability (opposite problem you have).
You might do better to examine your real circuit and question why is it oscillating, rather than questioning why the simulation doesn't. Many layout and construction issues can can instabilities. For example, you never need to decouple power supplies in the simulation since power rails and grounds are all perfect. When have you ever gotten away with that in a real circuit? Care to post a photo of your circuit?
(p.s., you did not attach the simulation).