There are several correct ways -- both of the methods you described are fine. I would suggest the first method, using gluLookAt or otherwise directly manipulating the view transformation matrix to transform it sideways. All parameters to gluLookAt are still going to be used, it's simply that certain combinations of values for those parameters will end up appearing to have an equivalent impact on the scene given that you eventually apply an orthographic projection.

GL combines the world and view matrices into one, so depending on the level to which you abstract that yourself it may not matter if you manipulate the "view" matrix or the "object" matrix (since they're the same). If you do maintain a separation of these concepts in your own code, I would say that it's more readable to manipulate the view matrix (via gluLookAt or more direct transformation) than the object matrix, even the math would end up being equivalent.

There are several correct ways -- both of the methods you described are fine. I would suggest the first method, using gluLookAt or otherwise directly manipulating the view transformation matrix to transform it sideways. All parameters to gluLookAt are still going to be used.

GL combines the world and view matrices into one, so depending on the level to which you abstract that yourself it may not matter if you manipulate the "view" matrix or the "object" matrix (since they're the same). If you do maintain a separation of these concepts in your own code, I would say that it's more readable to manipulate the view matrix (via gluLookAt or more direct transformation) than the object matrix, even the math would end up being equivalent.