Developing the dual model

I have the following linear program:

$$$$\min \sum_{\vec{s} \in S} \sum_{\vec{z} \in \Xi_{\vec{s}}} c(\vec{s}, \vec{z}) \times \chi(\vec{s}, \vec{z}) \label{eqADP4}$$$$ $$$$(1 - \lambda) \times \sum_{\vec{s} \in S} \sum_{\vec{z} \in \Xi_{\vec{s}}} \chi(\vec{s}, \vec{z}) = 1$$$$ $$$$\sum_{\vec{s} \in S} \sum_{\vec{z} \in \Xi_{\vec{s}}} \pi_{koie}(\vec{s}, \vec{z}) \times \chi(\vec{s}, \vec{z}) \geq \mathbb{E}_{\eta} [p^w_{koie}] \hspace{1cm} \forall k \in \mathcal{K}; o \in \mathcal{O}; i \in \mathcal{I}_k; e \in \mathcal{E}_k$$$$ $$$$\sum_{\vec{s} \in S} \sum_{\vec{z} \in \Xi_{\vec{s}}} \delta_{ktc}(\vec{s}, \vec{z}) \times \chi(\vec{s}, \vec{z}) \geq \mathbb{E}_{\eta} [p^m_{ktc}] \hspace{1cm} \forall k \in \mathcal{K}; t \in \mathcal{T}'; c \in \mathcal{C}$$$$ $$$$\chi(\vec{s}, \vec{z}) \in \mathbb{R}_{\geq0}$$$$

By associating variables $$y^1 \in \mathbb{R}$$, $$y^2_{koie} \in \mathbb{R}_{\ge0}$$ and $$y^3_{ktc} \in \mathbb{R}_{\ge0}$$ with the first, second and third constraint sets, respectively, I specify its dual model as follows:

$$$$\max y^1 + \sum_{k,o,i,e} y^2_{koie} \times \mathbb{E}_{\eta} [p^w_{koie}] + \sum_{k,t,c} y^3_{ktc} \times \mathbb{E}_{\eta} [p^m_{ktc}]$$$$ $$$$(1 - \lambda) \times y^1 \leq 0$$$$ $$$$\sum_{k,o,i,e} \pi_{koie}(\vec{s}, \vec{z}) \times y^2_{koie} + \sum_{k,t,c} \delta_{ktc}(\vec{s}, \vec{z}) \times y^3_{ktc} \leq c(\vec{s}, \vec{z}) \hspace{0.5cm} \forall \vec{s} \in S; \vec{z} \in \Xi_{\vec{s}}$$$$ $$$$y^1 \in \mathbb{R}, y^2_{koie} \in \mathbb{R}_{\ge0}, y^3_{ktc} \in \mathbb{R}_{\ge0}$$$$

However, I am not getting the same result! Please let me know if you can identify any mistakes.

Your first dual constraint is wrong. The term $$(1-\lambda)\times y^1$$ should be included in the left side of the second dual constraint.