Note that M1 current would be
I1= βn*W1/L1(Vgs-Vth)*(1+ΛVds)
but for M2 ΛVds would not have much effect as Vgs would be more dominating compared to Lambda ( Λ ) .
I2=βn*W2/L2(Vgs1-Vth)
Now if we assume Vds is more than Vgs then ΛVds would cause increase in current I1 also due to increased Vds i.e. Vgs1 ( for M2) would increase I2
I1 + I2 is constant so Vds would have to be at value closer to Vgs where ΛVds would not be significant.