How do I determine roasting temperature as a function of time?
I have not seen this discussed in terms of oven cookery, however, it is certainly a part of the conversation when cooking with sous vide.  Douglas Baldwin, noted expert, has a guide.  Here, I have linked his appendix, &quot;The mathematics of sous vide.&quot; Now, I am certain that you CAN NOT use this guide for oven cookery, because in the oven, you have a significant amount of evaporative cooling happening, which I think would dramatically change these calculations (I'm no mathematician).  However, I do include it to point out that the size and shape of your food must be taken into account.  You can't just consider time and temperature.
How do you know you need X minutes at Y degrees?  For how much lamb and bone?
I googled &quot;slow roasted leg of lamb.&quot;  There are plenty of recipes, I don't see anyone cooking them for 14 hours.  I think you can achieve the texture you want in much less time.  So, I doubt you need to be as precise as you are suggesting. You might err on the side of your roast being finished early, rather than late, but even if it were finished well before your guests arrived, that is workable for a delicious meal.