Climate-sensitive livelihoods in Sub-Saharan Africa face compounded risks from unpredictable rainfall, drought, and rising temperatures, yet current LVI-IPCC frameworks ignore carbon finance access as a determinant of adaptive capacity despite its growing importance in African climate policy. This paper introduces a carbon market access indicator that extends the LVI-IPCC framework and applies it to three livelihood systems in Migori County, Kenya: smallholder farming, artisanal fishing, and artisanal gold mining. The study used a desktop approach, drawing on secondary data (KDHS 2022, CHIRPS rainfall data, and county development plans) for eight wards to compute LVI-IPCC scores using Hahn et al.'s (2009) equal-weighted, min-max normalised sub-index method. An ordinal carbon market access indicator was incorporated into the adaptive capacity sub-domain, with scores computed with and without it as a robustness test. Fishing had higher LVI-IPCC scores (0.008) than mining and mixed agriculture (-0.003) and smallholder agriculture (-0.047). All three livelihoods scored zero on carbon market access despite their suitability for blue carbon, mercury-reduction and agroforestry pathways respectively. Adding the indicator worsened adaptive capacity deficits across all groups without changing their ranking. Carbon market exclusion emerged as a universal but differentiated adaptive capacity deficit, pointing to an important risk determinant omitted from aggregate vulnerability indices and relevant to county-level carbon finance planning and benefit sharing. Beyond its methodological contribution, the findings recast carbon market exclusion as a leadership-in-policy gap: an institutional capacity deficit that devolved climate governance structures are mandated, but not yet equipped, to close.