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This study presents a numerical analysis of the impact of hydrogen addition on the consumption speed of premixed lean methane-air laminar flames exposed to combined strain and heat loss. Equivalence ratios of 0.9, 0.7, and 0.5 with fuel mixture composition ranging from pure methane to pure hydrogen are considered to cover a wide range of conditions in the lean region. The 1-D asymmetric counter-flow premixed laminar flame aCFPF with heat loss on the product side is considered as a flamelet configuration that represents an elementary unit of a turbulent flame and the consumption speed is used to characterize the effect of strain and heat loss. Due to the ambiguity in the definition of the consumption speed of multi-component mixtures, two definitions are compared. The definition of the consumption speed based on the heat release results in lower values of the stretched flame speed and even an opposite response to strain rate for some methane-hydrogen-air mixtures compared to the definition based on the fuel consumption. Strain rate leads to an increase in the flame speed for the lean methane-hydrogen mixtures, reaching a maximum value after which the flame speed decreases with strain rate. Heat loss decreases the stretched flame speed and leads to a sooner extinction of the flamelet due to combined strain and heat loss. Hydrogen addition and equivalence ratio significantly impact the maximum consumption speed and the flame response to combined strain rate and heat loss. The effect of hydrogen on the thermo-diffusive properties of the mixture, characterized by the Zel'dovich number and the effective Lewis number, are also analyzed and related to the effect on the consumption speed. Two definitions of the Lewis number of the multi-component fuel mixture are evaluated against the results from the aCFPF.