I have been trying to find information about dyeing with Lemon Scented Eucalyptus and have not got very far. There is not a lot of information on the internet. I did find some information in some books I had but it is more about dyeing with eucalyptus bark, not specifically from the lemon scented tree.
However, I did find some information that was of use and have experimented with some silk sliver (also known as roving) and wool roving, as well as some pongee silk and small pieces of wool batting. I got quite a variety of colours, depending on what process I used and the mordants.
First I tried some old bark from the tree next door (yes, I do have restless nights sleeping under it on windy nights).
I collected the bark over a few months, so it was very dry and I did not have to take any from the tree. All the books I have been reading about dyeing with eucalyptus bark remind us strongly to try not to damage the tree. Taking bark from all around a tree will likely kill it.
The bark is not particularly dark but I hoped to get some colour from it.
I tried using some without pre-soaking, I just brought it to the boil and let it simmer for an hour. Then I drained it off and put in my bits and pieces.
They came out very pale. I used tissue silk, pongee silk and some wool batting (for quilting).