  High-accuracy composite wavefunction methods like Weizmann-4 (W4) theory,
high-accuracy extrapolated \textit{ab initio} thermochemistry (HEAT), and
Feller-Peterson-Dixon (FPD) enable sub-kJ/mol accuracy in gas-phase
thermochemical properties. Their biggest computational bottleneck is the
evaluation of the valence post-CCSD(T) correction term. We demonstrate here,
for the W4-17 thermochemistry benchmark and subsets thereof, that the lambda
coupled cluster expansion converges more rapidly and smoothly than the regular
coupled cluster series. By means of CCSDT(Q)$_\Lambda$ and CCSDTQ(5)$_\Lambda$,
we can considerably (up to an order of magnitude) accelerate W4- and W4.3-type
calculations without loss in accuracy, leading to the W4$\Lambda$ and
W4.3$\Lambda$ computational thermochemistry protocols.
