  The coupled quintessence model with disformal couplings is treated here to
mimic the $\Lambda$CDM background. Using this approach, the quintessence
potential does not have to be specified. The model considers a generic fluid
coupled to the quintessence, which is specified to be either dark matter or a
relativistic fluid. The background consists of a cosmological constant and
another uncoupled generic fluid, to cater for three studied scenarios. The
cosmological dynamics is investigated for the coupled quintessence model, whose
disformal couplings depend on the equation of state of both generic fluids. The
scenario, whereby both generic fluids are dark matter, was further analyzed for
an expansion history of the mimicking model. The analysis confirms that the
mass scale of the quintessence influences the disformal characteristics of the
dynamical system, which is portrayed by the evolution of an effective conformal
coupling.
