  We study inclusive $\Lambda_c^{\pm}$-baryon production in $pp$ collisions in
the general-mass variable-flavor number scheme and compare with data from the
LHCb, ALICE and CMS collaborations. We perform a new fit of the $c \to
\Lambda_c^+$ fragmentation function combining $e^+e^-$ data from OPAL and
Belle. The agreement with LHC data is slightly worse compared with a
calculation using an older fragmentation function, and the tension between
different determinations of $\Lambda_c^{\pm}$ production cross sections from
the LHC experimental collaborations is not resolved. The ratio of data for
$\Lambda_c^+$-baryon and $D^0$-meson production seems to violate the
universality of $c$-charm quark to $c$-hadron fragmentation.
