When did the behavior start? How does she respond to the consequences when you take the privileges away and is the behavior present at school or only at home?
Thank you for clarifying.
If the behavior takes place primarily at home it is either opportunistic and/or attention seeking.
A time out may not be something you'd want to use with her (She's older and that works better with toddlers) You would want to consequent her with things she finds important. For instance, if she likes a certain outfit/item, you may confiscate that. You can also deprive her of free play or TV time (anything that she finds pleasurable, you can use to take away) Of course, you may want to let her know how these items are to be earned back. Don't plan a long time frame (try to have her earn them back the same week)
Her lying may also relate to low self esteem (depending on whether or not she makes more stories that show her in favorable light) If that is the case, you can address the self esteem issue. If you believe that she is lying to get away with something (doing homework, chores, etc) then you address that. Behavioral is usually purposeful. Try to find out what purpose it serves to her. Even if it may be silly to an outsider, it always has a purpose for the person doing it.
Time out for her age range really would not be perceived by her as a consequence (some kids do not mind being removed from the environment and you've mentioned that she sings. Unless a removal from the environment is distressing to her, it is not a consequence.
It is typical to move onto the next item (but that may be a way to manipulate and show indifference so you do not take the stuff) Still confiscate whatever you believe will me missed by her.
Writing sentences over is not really something that shapes behavior. It is more like a punishment. You may instead assign her chores (things to help in the house) or even if you are to bring her to the grocery store with you with a list of things for her to gather into the shopping cart.
She should expect not just attention but positive feedback/compliments by a parent and being entrusted with small tasks around the house. That would be something to help her develop a sense of self sufficiency and belonging in the home.
The book below is not per se for step dads but is very good (you'd be a role model for her and teach her by example)
Joe Cucchiara (Author)