You'll have to be more specific about what you want to do,
in MD language. I don't know what self-propulsion means
in a fundamental physics sense. E.g. Newtons 3rd law.
Some questions:
1) How do you want to simulate the Janus particle? Is it point-like,
or are willing to represent it multiple particles? (In the later
case, standard Langevin dynamics equations would be enough to change
its direction randomly.)
2) Do you need to use an implicit solvent or are you content using an
explicit (perhaps coarse-grained) solvent?
3) Hydrodynamics:
  Most LAMMPS simulations I've seen use some kind of explicit solvent.
   LAMMPS does support Lattice-Boltzmann fluids, DPD and SRD:
http://lammps.sandia.gov/doc/fix_lb_fluid.html
http://lammps.sandia.gov/doc/pair_dpd.html
http://lammps.sandia.gov/doc/fix_srd.html
  Unfortunatley, what has not been done yet (too my knowledge) is
implement hydrodynamics in the limit of high Schmidt number.
(Typically this is done using an Oseen or Rotne-Prager-Yamakawa
tensor.) LAMMPS does not have support this yet. If you want to
implement this, we can point you in the right direction to get
started.
3) If you really want the particle to move with true constant speed
(random direction), and if you have multiple such particles, then I
think this would require editing the LAMMPS code. If you only have
one such particle, you might be able to get away with using fix
temp/rescale. (But that's not the way it was intended to be used.)
    But why do you need constant speed? (And how do you plan to
reconcile this with your desire to reproduce accurate hydrodynamics?)
Is this some kind of Brownian-ratchet?
4) Approximatley how many particles do you intend to have in your simulations?
   Keep in mind (the spatial decomposition) algorithms used in LAMMPS
were originally optimized for simulating systems with a large number
of particles, and (approximately) uniform density. However you don't
have to use it that way. (However I recall that GPU-enabled versions
of LAMMPS use a different decomposition algorithm. LAMMPS also has a
fix balance feature to help with non-uniform density simulations.)
You can write a fix in LAMMPS to do whatever you want
with particle velocities. Even violate Newton's laws.
You can even violate conservation of particle number (create and
destroy particles, although, again you may need to write your own fix
code).
Cheers
Andrew