Couple of thoughts.
The most important question is does she throw these tantrums at school (and how often). If essentially (compared to home) she does not do this at school (not talking about the lying here), then this is a behavior that she has learned will work for her at home and not at school. If this is true, it can be changed.
In terms of lying I am going to quote one of my older posts on the ADHD forum. It may not be true, but it is worth thinking about.
"Getting back to one of your original questions - as you well know kids with ADHD (when they are younger) really don't have very good filters. Hence they do things impulsively. It really doesn't take them very long (if they are intelligent) to figure out, that they are always getting blamed (probably correctly) by everyone and out of sheer survival instincts they lie. It happens all the time. Its not because of what you have done. Its because of what they have been experiencing for most of their life. "
I don't know that your daughter has any of the symptoms of ADHD or ADD. I do know that intelligent girls with ADD don't usually get noticed until about 4th grade when things like math (in particular) start getting to hard for them due to their inability to pay attention.
If you want some more information on this a book I highly recommend is, "The ADD/ ADHD Answer book," by Susan Ashley.
By the way, the standard method of dealing with (normal) tantrums is immediate timeouts until the tantrum ceases. Then and only then do you talk to them. Its very important that you realize you are breaking a learned behavior. It can take up to 28 days for this to happen according to experts, and this only works if you are very consistent. If she does not have these problems at school. It should work faster. If she does have these problems at school, then there is greater cause for concern. Hope some of this helps.
the tantrums could happen at anytime. when she doesnt get her way,when she doesnt like the rules, sometimes just playing with her or holding her hand in the store. the lies range quite a bit it could be about something she did wrong, blaming her brother for something she did, sneaking something example once at school something happened with another little girl i go talk to the teacher and tell her what my daughter said the teacher looks at her and says now you know thats not what u told me my daughter tells the teacher i know i told u i started it then with me standing right there my daughter tells me mommy i didnt do it and lies to us both while we r both standing with her. she has started having problems in school but she still is a A-B student and she is always embarrassed when she has to confront someone she did something wrong too.
Can you give instances of what she lies about also what triggers the tantrums ,? Has she shown any jealousy towrads her younger sister ...
Maybe when she says "I can't help it," she is being honest. I would have her evaluated to see what is going on. It's been going on for a long time and not improving.