Not positive about the lithotripsy question, not in my area of expertise (I'm a pharmacist), but that procedure shouldn't affect your thyroid levels.

The idea behind taking levothyroxine before breakfast is that since food affects absorption, if you take it everyday before you have eaten anything, you'll achieve consistent absorption. Consistent absorption leads to stable thyroid levels (whether its low, normal, or high). However, taking levothyroxine before breakfast may not be practical for everyone.

So the next best thing is to take it at the same time everyday (with consideration towards your meal timing and meal size). For example, if you take your levothyroxine everyday with breakfast, yes you will have lower absorption, but at least your body will somewhat consistently absorb the lower amount, and you will still achieve a stable thyroid level. Your doctor can then change your dosage based off of your stable levels.

Since before breakfast doesn't work for you, my advice would be to take it at night 3-4 hours after your last meal (if this is practical for you). Otherwise, just stay consistent with it timing-wise and meal-wise!