Hi, I have a dataset like this:

              Subject_ID Treatment Duration Pasient_Kontroll Age    CTP_NPC
 NSC-2019-290      K5137      DMSO   6hours          Control  47 0.28845794
 NSC-2019-291      K5039      DMSO   6hours          Control  62 0.06154937
 NSC-2019-292     K50128      DMSO   6hours          Control  45 0.25351167
 NSC-2019-293       U815      DMSO   6hours          Patient  32 0.22540896
 NSC-2019-294       U793      DMSO   6hours          Patient  23 0.25467268
 NSC-2019-295       U162      DMSO   6hours          Patient  38 0.20031763
 NSC-2019-299      K5137      DMSO    1week          Control  47 0.21114240
 NSC-2019-300      K5039      DMSO    1week          Control  62 0.11281822
 NSC-2019-301     K50128      DMSO    1week          Control  45 0.23429267
 NSC-2019-302       U815      DMSO    1week          Patient  32 0.20184951
 NSC-2019-303       U793      DMSO    1week          Patient  23 0.35476381
 NSC-2019-304       U162      DMSO    1week          Patient  38 0.19938699
 NSC-2019-308      K5137        Li   6hours          Control  47 0.30317057
 NSC-2019-309      K5039        Li   6hours          Control  62 0.28853031
 NSC-2019-310     K50128        Li   6hours          Control  45 0.31602120
 NSC-2019-311       U815        Li   6hours          Patient  32 0.42000711
 NSC-2019-312       U793        Li   6hours          Patient  23 0.36429453
 NSC-2019-313       U162        Li   6hours          Patient  38 0.37220548
 NSC-2019-317      K5137        Li    1week          Control  47 0.18130258
 NSC-2019-318      K5039        Li    1week          Control  62 0.12880417
 NSC-2019-319     K50128        Li    1week          Control  45 0.31397647
 NSC-2019-320       U815        Li    1week          Patient  32 0.14236717
 NSC-2019-321       U793        Li    1week          Patient  23 0.28045362
 NSC-2019-322       U162        Li    1week          Patient  38 0.30689310

I.e., 6 donors: 3 controls and 3 patients. For each donor, we have generated iPSC-derived NPCs and split these into 4 samples before running RNA-seq. One sample treated with DMSO (control treatment) for 6 hours, one sample treated with lithium (Li) for 6 hours, one sample treated with DMSO for 1 week, and one sample treated for lithium for 1 week. In total, 24 samples.

We want to identify the genes that are DE between Li-DMSO at 6 hours and Li-DMSO at 1 week across patient/control status (i.e. different treatment response in patients and controls) while adjusting for age and CPT_NPC effects. I understand that this is a very complex design (including paired samples), and I have not seen anyone do something similar before. What would be the appropriate R package and procedure? Any help is highly appreciated.

I would take a look at DESeq2's vignette. There are also useful examples given at the end of the manual page for results(), accessible via ?results.

In summary, you can do what you want by merging 2 or more of the metadata columns, and creating an interaction. A quick look tells me that you could probably do:

~ Treatment_PasientKontroll + Duration + Treatment_PasientKontroll:Duration + Age + CTP_NPC

Here, Treatment_PasientKontroll is a merged variable.

Kevin