Hey there,
The Blog page uses the Primary menu. Please set the menu you want for your blog page as Primary menu in Appearance > Menus > Manage Locations.
There is no option to set a unique menu for it. It is possible with the Pro theme because you can build a unique for different pages including the blog page.
Another way is through custom development. Regretfully, this would be outside the scope of our support. We do have an in-house custom development team that offer paid services, who may be able to assist. They can be contacted at [email protected] if this is of interest to you.
Thanks.