When retrieving a BlockData object (of type org.bukkit.block.data.type.Sign) from an Sign block(org.bukkit.block.Sign), the returned BlockData has no method to get or set the lines of the sign-data, even though this would be expected.
Even wore(I assume this is a result of the previous issue) when the getAsString() method is used on the BlockData the line-information is not contained within the output and therefore completely inaccessible.

//This basically serves as a minimal reproduction plugin.
Block b = null; // Initialized with a valid sign-block
BlockData blockData  = b.getBlockData();
String blockDataString = blockData.getAsString();
Bukkit.getLogger().info(blockDataString);

This code logs:
minecraft:oak_sign[rotation=0,waterlogged=false]

while F3+I returns:
/setblock -9 38 10 minecraft:oak_sign[rotation=0,waterlogged=false]{Color:"black",Text4:'{"extra":[

],"text":""}',Text3:'{"extra":[

],"text":""}',Text2:'{"extra":[

],"text":""}',Text1:'{"extra":[

],"text":""}'}

Resolving this issue would also be a good opportunity to add an API to set click-actions for signs to, but that is by no means needed to resolve the bug addressed in this issue.