I just have to make sure that the lab values I read match the positions of the ti2 (no1 is in position K11 in my read Lab values).
Exactly. And txt2ti3 cares about the rest (formating, adding additional header fields like COLOR_REP, ...). The CIE values (i.e. XYZ or Lab values) in the ti2 file are just estimated (used for reading validation purposes). You have to replace them with your measurement data to get a meaningful printer ti3 file.