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If we have an interface, say LaAlO3/SrTiO3, often, it is mentioned that we hold the in-plane lattice constants and allow the growth direction to relax. Does this imply selective dynamics with ISIF 2 or something else?

If you have a vacuum region then that is exactly what you need to do.
If it is a repeated layer structure you need to optimize the z direction as well. Then you could setup multiple calculations with different heights, relax the positions and the lowest energy structure is the most stable one.

If I didn't get it wrong and you are trying to relax only one lattice vector while keeping the other two fixed, maybe give this a try? https://github.com/Chengcheng-Xiao/VASP_OPT_AXIS

I was trying to benchmark a SrTiO3-LaAlO3 system of 9 (SrO + TiO2) and 5 LaAlO3 (LaO + AlO2) layers, but I am not getting the required DOS at the interface whereas the surface DOS seems to be very in agreement with what is available in the literature. I have given a 15 A vacuum to prevent interactions and performed with as well as without dipole corrections. Is there something I am missing while making the structure or performing normal SCF calculations and thereafter DOS. I am attaching the files for scf here, if anyone can suggest anything.

Note: I have fixed the two layers of SrTiO3 in one of them to give a bulk like effect, which is also mentioned in some of the literatures.

I have attached it here, missed it in the previous reply.

Sorry, but your input is not specific enough. You mention that the DOS looks wrong, but you do not provide the input/output of that calculation. Also could you clarify better what you see and what you expect, please? These calculations with very long cell are very sensitive, because there may be local minima that you can run into.
You may also want to plot the potential (LVTOT) and make sure that it looks like what you expect. In particular, make sure that the potential has a kink in the vacuum region.