If you just want the hydrodynamics, without making any other changes
to your system, the traditional way to do this is to represent the
solvent implicitly and use an Oseen-like (Rotne-Prager-like) tensor
approach to approximate hydrodynamic behaviour. Unless I'm mistaken,
LAMMPS can't do this.
I did a quick search on google to find a free publicly available MD
simulation program that can do this and have not located one yet.
Perhaps someone else can suggest one.
(I know that AMBER7 used to have this feature. I don't know if the
newer versions do.)
---- alternate approaches ---
I don't know how to use SRD. I quickly skimmed the documentation for
SRD (as described in the lammps manual). It seems that SRD particles
are more like gas particles than a liquid because they don't interact
with each other.
Consequently, if you want hydrodynamic interactions, then there is no
way to do this using SRD. (Perhaps I am misunderstanding you, when
you say that you want "hydrodynamics".)
As an alternative, you could fill your box with a dense liquid. (Fill
it with particles which do interact with each other). But this is
much slower than "SRD". And this will probably drastically change
your system in other ways (both energetically, and entropically, even
if the interactions are purely repulsive). If you want to do this,
you would need to select your solvent model carefully.
I am not an expert (and have not used) any of these methods, so I hope
I am not misleading you.