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I've searched all options in Line format, and I can make it dotted or change the arrow heads, but it seems impossible in my LibreOffice 5.0.3.2 to draw something as simple as a double line for an arrow, to get something like

LibreOffice Draw has no option for "double lines" yet, as LibreOffice 5.3.

Custom line styles: Not relevant

This article on LibreOffice Help has noted how to use custom line style from target file.

To load a line styles file:

1. Choose Format - Line, and then click the Line Styles tab.


2. Click the Load Line Styles button.


3. Locate the file containing the line styles that you want to load, and then click OK. The file has the format [filename].sod.

To save a line styles file, click the Save Line Styles button, enter a filename, and then click OK.

While .sod file seems to be useful for saving and loading modified line styles, there is no relevant information to create one from new.

Custom arrow with double lines

There are several workarounds to create an arrow with double lines.

1. 
   Workaround A (easy): Use Unicode character


2. 
   Workaround B: Use merged objects

Workaround A (easy)

Use Unicode character that is found in Unicode Block "Arrows". For example, there is U+21D2 RIGHTWARDS DOUBLE ARROW that represents ⇒ character.

1. In Drawing toolbar, select "Text Box" and draw a text box.




2. Type the Unicode character: Press key combination Ctrl+Shift+U, then press 2 1 D 2 and finally press Enter. This will insert ⇒.




3. Finally, adjust size of the character text font and text box.

Workaround B

Use several drawing objects and merge together to reproduce the arrow with desired style. The following steps will explain for arrow with double lines.

1. In Drawing toolbar, select "Line ends with arrow" and draw the line; Keep the arrow small, such that only the arrow end is visible and the line is hidden underneath.




2. Select the object, Format (or right-click menu) ➜ Lines... ➜ Line tab - Line Properties, then change Width to 0.04"; under Arrow Styles, change End style to "Arrow Concave" and arrow width to 0.30" (the order of changing is important).




3. In Drawing toolbar, select "Insert line" and draw the line; The length of line is user's choice.




4. Select the object, Format (or right-click menu) ➜ Lines... ➜ Line tab - Line Properties, then change Width to 0.04".




5. Make a copy of line from step 4.




6. Place the lines appropriately with respect to the arrow.




7. Select all objects, then Modify (or right-click menu) ➜ Shapes ➜ Merge.

The following screenshot combo shows how the arrows would look like.

Using either workaround has one drawback: resize does not work like built-in objects.

For example, horizontal resizing of the merged object will cause the arrow end to be stretched instead of only the line becomes longer. Therefore, to have a longer line, the length should be adjusted beforehand (Workaround B, step 3).

Unlike Group action that groups objects, the Merge action creates merged object that can be resized as whole. However, the only way to revert Merge action is "Undo" or Ctrl+Z (there is no “Unmerge” menu) at time of edit. Users are advised to make several copies of objects before merging objects, in case the end result becomes unexpected and has too many steps to "Undo".

Tested using LibreOffice 5.3 in Xubuntu 14.04.