What kind of iron has your sister been prescribed? What dosage and how many per day?
My ferritin was very low last year and I had the dreadful breathlessness, yawning and fatigue that your sister suffers from. I got a prescription from my doctor (very reluctantly and begrudgingly) for :
Ferrous fumarate 210mg, to be taken 3 times per day. The prescription was enough for 8 weeks. The pills come in boxes of 84 - enough for three pills a day for 28 days.
I discovered quite by accident when I collected the pills that I could buy the ferrous fumarate without a prescription. (I've since discovered that Boots insist on a prescription, but Lloyds and some other pharmacies don't.) Each box of 84 pills costs just over £4 from Lloyds.
Taking iron pills gives many people constipation. The best way of dealing with this is to take each iron pill with 500mg - 1000mg of vitamin C, because vitamin C loosens things up. The vitamin C also has the advantage that it helps your body to absorb the iron.
I would suggest your sister takes her levo first thing in the morning before breakfast. Then she could take her iron after lunch, after her evening meal and just before bed. Alternatively she could take her levo at night and take the iron earlier, but personally I always found that impossible to fit in. The important thing to be aware of is to keep the levo and the iron separated by four hours.
Building up iron can take some people a very long time. I had blood tests done after about 6 months and my ferritin had improved but still wasn't brilliant, and my iron and haemoglobin were still very low in range.
If your sister has problems tolerating the iron she has been prescribed, then be aware that there are many other ways of taking it, and other iron compounds which work. It is just trial and error to find what works.