  The singly-ionized lutetium has a number of fortuitous properties well suited
for a design of an optical clock and corresponding applications. In this work,
we study Lu+ properties relevant to a development of the clock using the
relativistic high-precision method combining configuration interaction and the
linearized coupled-cluster approaches. The systematic effects due to
interaction of an external electric-field gradient with the quadrupole moment
and the dynamic correction to the blackbody radiation shift are studied and
uncertainties are estimated. The value of the 5d6s 1D_2 polarizability is
predicted. We also demonstrate that Lu+ is a good candidate to search for
variation of the fine-structure constant.
