I think what you want to do is:
- Start with the line chart that has the single line with the correct coloring
- Drag and drop "Type" on DETAIL
- This should create one line for each of the TYPE values and keep the coloring
- Drag and Drop "Type" on LABEL
- This will put the Type name on each line
Using this method, I was able to get what I think you are looking for on some sample data I have. If this does not work for you, post your viz in TWBX format as it makes things easier to have your exact scenario
That worked! Thank you!