Changing the line type in the ggplot legend

To use your original data frame you should change to lines. In both calls to geom_line() put linetype= inside the aes() and set the type to variable name.

 + geom_line(aes(y = Mean, color = "Medelvärde",linetype = "Medelvärde"), 
            size = 1.5, alpha = 1)  
 + geom_line(aes(y = N, 
                color = "Antal Kassor",linetype="Antal Kassor"), size = 0.9, alpha = 1)

Then you should add scale_linetype_manual() with the same name as for scale_colour_manual() and there set line types you need.

+scale_linetype_manual("Variabler",values=c("Antal Kassor"=2,"Medelvärde"=1))

Also guides() should be adjusted for linetype and colours to better show lines in legend.

+ guides(fill = guide_legend(keywidth = 1, keyheight = 1),
    linetype=guide_legend(keywidth = 3, keyheight = 1),
    colour=guide_legend(keywidth = 3, keyheight = 1))

Here is complete code used:

theplot<- ggplot(subset(hej3,variable=="Delägare.män."), aes(x = Year)) + 

  geom_line(aes(y = Mean, color = "Medelvärde",linetype = "Medelvärde"), 
            size = 1.5, alpha = 1) + 

  geom_ribbon(aes(ymax = Max, 
                  ymin = Min, fill = "Delägare Män Max/Min"), linetype = 3, 
              alpha = 0.4) + 

  geom_ribbon(aes(ymax = Mean+sd, ymin = Mean-sd, fill = "Mean +- sd"), 
              colour = "grey50", linetype = 3, alpha = 0.8)+

  #geom_line(aes(y = Sum, 
  #color = "Sum Delägare Män"), size = 0.9, linetype = 1, alpha = 1) + 

  geom_line(aes(y = N, 
                color = "Antal Kassor",linetype="Antal Kassor"), size = 0.9, alpha = 1)+

  scale_y_continuous(breaks = seq(-500, 4800, by = 100), limits = c(-500, 4800), 
                     labels = seq(-500, 4800, by = 100))+ 
  scale_x_continuous(breaks=seq(1901,1930,2))+
  labs(title = "Manliga Delägare i Yrkeskassor") +

  scale_color_manual("Variabler", breaks = c("Antal Kassor","Medelvärde"),  
                     values = c("Antal Kassor" = "black", "Medelvärde" = "#6E6E6E")) + 
  scale_fill_manual(" Ribbons", breaks = c("Delägare Män Max/Min", "Mean +- sd"), 
                    values = c(`Delägare Män Max/Min` = "grey50", `Mean +- sd` = "#4E4E4E")) + 
  scale_linetype_manual("Variabler",values=c("Antal Kassor"=2,"Medelvärde"=1))+
  theme(legend.direction = "horizontal", legend.position = "bottom", legend.key = element_blank(), 
        legend.background = element_rect(fill = "white", colour = "gray30")) + 
  guides(fill = guide_legend(keywidth = 1, keyheight = 1), linetype=guide_legend(keywidth = 3, keyheight = 1),
         colour=guide_legend(keywidth = 3, keyheight = 1)) +
     coord_cartesian(ylim = c(-300, 600))