The cosmological constant is the parameter $\Lambda$ in the Einstein equation:
$$ G_{\mu\nu} + \Lambda g_{\mu\nu} = 8\pi T_{\mu\nu} $$
and it is by definition a constant, so it cannot change. I think it is best regarded as a geometrical property of the universe (though other views exist) which is why it's normally put on the left hand side of the equals sign.
However the observed acceleration of distant galaxies may be due not to a cosmological constant but to a scalar field called quintessence. This can change, and indeed there have been lots of theories about might be generating the quintessence field, what its properties are and how it might change with time.
To study this, attempts are being made to get very detailed data on the galaxy distance — recession velocity relationship. In principle the exact form of this could distinguish between a cosmological constant and quintessence.
If you're interested in pursuing this further Lawrence Krauss' book is a good starting point.