Diagnosing what is causing the lethargy is key... eggs are good in moderation.. loaded with nutrients and easy to digest. However they are 34% protein and a whopping 64% fat... which could lead to a whole host of other problems.
So When was the last time your hen laid an egg? **8 hens with her. She lays blue eggs as do 2 others. No blue eggs in about a week. Tough to tell when she did.
Is she pooping? **What does it look like? Very watery. I assume because she has not been eating much and just drinking with bit of nibbles.
Are you able to check her crop and see if it is empty in the morning before she has access to feed and water? **Can do if I get up earlier then they do

It was full this evening after 2nd egg mash.
What is your regular feed? **Mega Layer pellet. Black oil sunflower seeds were added about 3 weeks ago. They (1 Roo and 8 hens) get about 3 small hand fulls throughout the day added around the feeder and I mix some into the feed.
How many others in the flock? **9
Current weather? **Coolish (14 night and tops in lows 20s duing day).
Ever worm or have a vet you can take a fecal float to? **Been doing DiamT. earth in feed every couple weeks. Not given an actual dewormer.
What breed is she? **Cream crest Legbar
Any recent addition to your flock? **No. New hens in another barn about 2 weeks ago. No contact at all. Those hens have been laying well and very healthy since arrival.
Can you use a flashlight and check after dark for parasites like lice/mites. **Not seen anything when looking but not looked in dark with flashlight. Can try that tomorrow.
Also get a good look at her vent, is it clean or caked, regular flesh colored or swollen or angry looking? **Looks normal.
Is she staying with the flock when they forage or where is she hanging out at? **Goes out with them in the morning to a very large grass run. Its all grass with some sand in a couple spots. No mud or muck. She was in the coop mid day pecking around the feeder by herself. Not in the feeder though, just the small pieces around it.
Adding your general location to your profile can help others to make the best suggestion possible at a glance.

**Ontario Canada.
Poultry nutri drench has some amino acids in addition the vitamins and such. It's really one of the best supplement products on the market and a good choice if a boost is needed. **I did give her some of this today directly into mouth. She took it well.
I suggest avoiding tossing all kinds of fixes at what you aren't sure of as far as herbal remedies and such and work to get to the roost cause instead of possibly masking symptom or adding to them. Sounds like you have done just about all you can as far as support goes! Answering the questions might help us get clues so we can try and help our best to.