Hi Stella, yes, lemon and citrus can be very harmful to dogs. Dogs normally don't like the sour taste of lemons, however any part of tree can pose a danger to them.

Your dog might get ill from eating any part of a lime and lemon tree – leaves, peel, or fruit – since they contain psoralens compounds and essential oils like limonene and linalool which are toxic to dogs.

Read the full article:

https://uscitrus.com/blogs/citrus-simplified/can-dogs-eat-citrus-a-complete-guide-on-citrus-poisoning

have a careful look at the stems for scale insects. its odd that the plant is dripping a sugary liquid. that sounds like 'honeydew' which is the waste from scale insects or aphids.

Citrus is toxic as Bathgate says. as for the honey dew I am not sure as it is usually just excess sugars that have passed through the gut of the insect. I wouldn't take the risk to be honest.

My feeling is that if the aphids are ingesting the sap from the tree, then the honeydew they excrete may still contain traces of the toxic compounds. I would err on the side of caution - not for my dog.