Unfortunately, it’s impossible to map a lookup field on a choice field. There’s a workaround, however, by using a calculated field which copies the information from the choice field. The look up field is then able to map the calculated field’s value.
Start out by creating 2 custom lists; One list where the choice and calculated columns reside:
And another list where the lookup will be done:
Navigate to the list with content, and click on the “List” contextual tab in the ribbon. With the list options open, click on the “Create Column” button. When the dialog pops up fill in the desired options and select “choice” as column type:
Click on OK. The choice column should now be added to your list. Click the “Create Column” button again, but now select “Calculated” as column type:
Scroll down and reference the choice field in your calculation formula:
Click OK. The calculated column should now be added to your list with content. Add a new item to check whether the calculation formula works:
Navigate to the list where the lookup will be made and create a new column. Fill in a desired name and select “Lookup” as column type:
Scroll down again, and select your list with content where the lookup column should get its information. Next, select the title to be looked up and as you can see, the calculated column shows up as a selectable property:
Finish adding the column by clicking OK. Whenever you add a new item to the lookup list and use the lookup column, the chosen choice field from the content list will be shown:
In an ideal situation, Microsoft addresses this issue and makes choice fields able to be looked up in the near future.