Wash then asparagus then trim the ends off and discard. Peel the skin from the asparagus stems, apart from the tips, but don't discard the peelings.
Place the asparagus peelings in a pot and add the water. Cover, place over a medium heat and bring to a simmer. Reduce the heat slightly and simmer for around 20 minutes.
As the peelings are simmering to make the asparagus stock, chop the asparagus stems into chunks, about 1 ½ (3cm) in length. Cut the tips off first, set them to one side then chop the rest.
Pour the asparagus stock through a strainer/sieve into a bowl, reserving the liquid and discarding the peelings.
Return the stock to the pot and add the asparagus chunks from the main part of the stem - don't add the tips at this point. Return to the stove and simmer over a medium heat, covered, for around 8 minutes. Then, add the tips and simmer another 6 minutes or so until the asparagus is tender.
Strain the liquid again, this time saving the asparagus and setting to one side. Keep the stock in the bowl for now.
Wipe down the pot, if needed, then add the butter over a medium heat. Once it has melted and starts to bubble, add the flour and stir so that they combine. Continue to cook for another couple of minutes until the paste becomes gently brown and starts to smell a bit nutty.
Gradually add the stock, just a little at a time, and stir constantly to incorporate it into the flour paste (the roux). Keep adding, little by little, and mix to keep the paste smooth as it gradually thins out. If needed, whisk a little to remove any lumps.
Once all of the liquid has been added and the soup has a good consistency, add the lemon juice. Taste the soup to check the seasoning and, if needed, add a little more lemon or salt.
Add the cream and stir through. Then, divide the cooked asparagus between two bowls (making sure each has roughly the same amount of tips and overall). Pour over the soup and serve.