  This paper discusses a generalized model for compact stars, assumed to be
anisotropic in nature due to the spherical symmetry and high density. After
embedding the four-dimensional spacetime in a five-dimensional flat spacetime,
which may be treated as an alternative to Karmarkar's condition of embedding
class 1 spacetime, the Einstein field equations were solved by employing a
class of physically acceptable metric functions proposed by Lake
\cite{Lake2003}. The physical properties determined include the anisotropic
factor showing that the anisotropy is zero at the center and maximal at the
surface. Other boundary conditions yielded the values of various parameters
needed for rendering the numerous plots and also led to the EOS parameters. It
was further determined that the usual energy conditions are satisfied and that
the compact structures are stable, based on several criteria, starting with the
TOV equation. The calculation of the effective gravitational mass shows that
the models satisfy the Buchdahl condition. Finally, the values of the numerous
constants and physical parameters were determined specifically for the strange
star LMCX-4. It is shown that the present generalized model can justify most
off the compact stars including white dwarfs and ultra dense compact stars for
a suitable tuning of the parametric values of $n$.
