  If kinematically accessible, hadron collider experiments provide an ideal
laboratory for the direct production of heavy lepton partners in Seesaw models.
In the context of the Type III Seesaw Mechanism, the $\mathcal{O}(\alpha_s)$
rate and shape corrections are presented for the pair production of
hypothetical, heavy $SU(2)_L$ triplet leptons in $pp$ collisions at $\sqrt{s}=$
13, 14, and 100 TeV. The next-to-leading order (NLO) $K$-factors span,
approximately, $K^{NLO}=1.1 - 1.4$ for both charged current and neutral current
processes over a triplet mass range $m_T = 100~\text{GeV}-2~\text{TeV}$. Total
production cross sections exhibit a $^{+5\%}_{-6\%}$ scale dependence at 14 TeV
and $\pm1\%$ at 100 TeV. The NLO differential $K$-factors for heavy lepton
kinematics are largely flat, suggesting that na\"ive scaling by the total
$K^{NLO}$ is reasonably justified. The resummed transverse momentum
distribution of the dilepton system is presented at leading logarithmic (LL)
accuracy. The effects of resummation are large in TeV-scale dilepton systems.
Discovery potential to heavy lepton pairs at 14 and 100 TeV is briefly
explored: At the High-Luminosity LHC, we estimate a $4.8-6.3\sigma$ discovery
potential maximally for $m_T = 1.5-1.6~\text{TeV}$ after 3000 fb$^{-1}$. With
300 (3000) fb$^{-1}$, there is $2\sigma$ sensitivity up to $m_T =
1.3-1.4~\text{TeV}~(1.7-1.8~\text{TeV})$ in the individual channels. At 100 TeV
and with 10 fb$^{-1}$, a $5\sigma$ discovery can be achieved for
$m_T=1.4-1.6~\text{TeV}$. Due to the factorization properties of Drell-Yan-type
systems, the fixed order and resummed calculations reduce to convolutions over
tree-level quantities.
