  Measurements are presented of the production of primary K(S)0 and Lambda
particles in proton-proton collisions at sqrt(s) = 7 TeV in the region
transverse to the leading charged-particle jet in each event. The average
multiplicity and average scalar transverse momentum sum of K(S)0 and Lambda
particles measured at pseudorapidities abs(eta) < 2 rise with increasing
charged-particle jet pt in the range 1-10 GeV and saturate in the region 10-50
GeV. The rise and saturation of the strange particle yields and transverse
momentum sums in the underlying event are similar to those observed for
inclusive charged particles, which confirms the impact-parameter picture of
multiple parton interactions. The results are compared to recent tunes of the
PYTHIA Monte Carlo event generator. The PYTHIA simulations underestimate the
data by 15-30% for K(S)0 mesons and by about 50% for Lambda baryons, a deficit
similar to that observed for the inclusive strange particle production in
non-single-diffractive proton-proton collisions. The constant strange- to
charged-particle activity ratios and the similar trends for mesons and baryons
indicate that the multiparton-interaction dynamics is decoupled from parton
hadronization, which occurs at a later stage.
