T4 should be done in fasted state but it will absorb even having breakfast, milk and coffee (You will absorb 20-50% less, thats all).
So if you dont like to wait you can always adjust your dosage with bloods. Some patients take 150mg t4 because they are not fasted when they could really achieve the same medical results with just 75-100 but taking it fasted.
I think t3 dont require any specific condition.
Ill take half dose of t3 AM with your t4 (fasted, at least 30min), and the other half of t3 in PM.
Adjust accordingly with bloods. If i were you ill have 2 bloods. One fasted 12h post last t3 dose, to see your minimun ft3 levels and the other one 2-4h post t3 dose to see the peak ft3 level. You dont want to be above high-normal range in any case (even at peak). Ill look for stable levels.
As you can see here:
https://www.liebertpub.com/doi/10.1089/thy.2019.0101?url_ver=Z39.88-2003&rfr_id=ori:rid:crossref.org&rfr_dat=cr_pub 0pubmed
Higher and more stable levels are achieved using t3+t4 (splitting t3 dose AM/PM).
FIG. 4. A PK modeling of 50 mcg of LT3 administered on a thrice (
A), twice (
B), or single (
C) daily regimen was generated. Solid lines: reference range of T3. Dashed line: mean concentration of T3. All the proposed treatment schemes result in mean T3 concentrations near the upper limit of reference range, but with dramatic differences in the variance (
see Results for details).
FIG. 5. A PK modeling of LT3/LT4 combination therapy with 3.25 (
A), 5 (
B), and 10 (
C) mcg of LT3 administered on a twice-daily regimen was generated. Solid lines: reference range of T3. Dashed line: mean concentration of T3 (
see Results for details).