Yes eggs are pretty high in Lysine as well as many other poultry foods such as chicken.
Some other foods that are high in Lysine are Cheese, red meat, pork, Parmasen Cheese as well as cod and sardines.
If you need to increase your Lysine intake then eating eggs or any of the other foods can help you increase your Lysine levels.
You can also buy over the counter Lysine supplements to take that can help raise your Lysine levels when you're suffering from a Lysine deficiency.
I take some Lysine Supplements myself after my doctor suggested it and you don't need a prescription for them as Walmart sells some cheap Lysine Supplements that you can buy over the counter.