No, you cannot perform a second LR-TDDFT calculation with a reference built from the CI vectors of an excited state. LR-TDDFT is formulated for a single determinant reference state and your T2 solution from the first LR-TDDFT would be a linear combination of determinants.
Quadratic response TDDFT could give you the absorption spectrum for an excited state; however, it is not implemented in NWChem (the only implementation I am aware of is in the code Dalton).
Within NWChem, you could attempt our RT-TDDFT based approach to excited state absorption ("Excited state absorption from real-time time-dependent density functional theory" JCTC vol. 11 4294-4303 [2015]
https://pubs.acs.org/doi/abs/10.1021/acs.jctc.5b00473). While not documented, the functionality for this approach is in version 6.8 of the code. You would need to first run a LR-TDDFT gradient calculation on the excited state of interest in order to generate the excited state density matrix (or matrices in the case of an open shell calculation). You can then use the excited state density as your starting point by adding the appropriate load command to your RT-TDDFT input block:
load density <file name>.dmat
for closed shell or
load density <file name>.dmatA <file name>.dmatB
for open shell, where you would obviously insert the file name for the density matrix (matrices) generated from the LR-TDDFT gradient calculation. From there you should be able to follow the method outlined in the above cited paper to generate the absorption spectrum.