Lily
In VFL, lily means beauty, sweetness, elegance - that kind of stuff. A lily is a flower that is very easy to grow as long as it is planted in the right place. Severus was not her right plac, but James was..
Lilies make wonderful cut flowers. Severus is a pun off of the word sever. Once he cut their friendship, her life was much better.
Petunia
In VFL, petunia can mean resentment and anger, which is very fitting considering how she resented magic and how her parents loved her sister. (Some of the websites I've been to say that petunia means "your presence soothes me." I'm not quite sure what that could mean.)
A petunia is a flower that needs shelter from the wind, and is best grown in a basket. It's very representative of the fact that she can't imagine anything outside her perfect normal world.
Severus
You've all heard that quote about asphodel and wormwood.
Asphodel is a type of lily that means "my regrets follow you to the grave." So really you don't need the wormwood to get your point across. (But it does help.)
Snape also asked Harry what the difference between monkshood and wolfsbane was. (In case you've forgotten, it's the same thing.) I've derived several meanings from this. Monkshood is associated with chivalry, which is what Medieval people (from England) called their knights. Today it is associated with bravery.
Wolfsbane indicates misanthropy. That word means "a dislike of humankind" according to Google. Combining these two could give you:
1. The fact that Snape hates James, who was put in Gryffindor for a reason.
2. The fact that Snape just generally hates Gryffindor.
3. Wolfsbane was known as poison to werewolves in myths, so I wonder if this could have something to do with Remus (I need to research monkshood more).