Once your thyroid levels - free T4 and free T3, not just TSH - are ideal for your body's needs, your cholesterol should come down within a few months. But with TSH of 7, you certainly aren't there yet.
At the onset of my thyroid treatment, my numbers were:
Total ------ LDL------ HDL
231 ------- 148 ----- 51
After I reached my optimal dose/levels a year later, my numbers were:
Total ------ LDL------ HDL
212 ------- 115 ----- 62
These improvements happened just from thyroid treatment, no other changes in diet and/or exercise. But my starting TSH was only 7, so it's possible you may see even greater improvement than I did. I hope so!