I have had several dreams of Lions surrounding me and they always seem friendly but are chasing me. I feel afraid and in my dreams I'm always trying to escape.  There are usually
a few Lions and every where I turn they are there.  What do think it means?

it helps to have a dream symbol book by your bedside; it helps to figure out what the symbols mean. however, for my opinion, the lion is king of beasts. there is hardly any predator which can defeat the power and strength of this animal. I'd say the power of this leader of the beasts is within you but you will not embrace the power you have and so u run away. nonetheless, you cannot flee from yourself. if you look into the eye of the lion you will see much beauty, as if there is an ocean of wisdom in their eyes. they own themselves. they make no excuses or apologies. study the wisdom of the lion. it may be your totem, your special symbol to embrace. love, alysia

Yes Alysia gives good hints Marguerite!
Concerning repeating dreams in general, the standard advice is to try to make a change at one point of it and see what's happening. You could imagine when awake such a change, for example to imagine to be with lions and let one come near to you, the friendliest seeming, careful with respect, and let love flow. Then maybe this dream, when it's occuring again would change too and maybe the lion is telling you something or you just become friends.

A woman I met had a lion as their spiritual helper.

Spooky

You could try doing some dream journaling.  Give one of the lions, or them as a collective, a voice and let them speak.  Ask a question, like why are you chasing me?  Then just free flow write whatever comes to mind.  Don't think about your writing, don't worry about spelling and such, just try to let it flow.  Then ask another question, and so on.  If you see a flow of thought going, just go with it.  

If you don't feel comfortable writing, you can do the same thing in your mind.  Just imagine having a conversation with one of these lions.  You may feel like you are just making it up, but the point is to just go along with it and see what happens.  You will find that the free flow of thought comes so fast and naturally that after you are done, you will realize that you weren't having to try and make up stuff, it just came naturally.  With dream analysis in this way, you are really unlocking things you've hidden from yourself.  It really works.