- This sentence is ungrammatical.
The whole sentence is a CP, the NP lies was extracted from an embedded VP-shell to the uppermost Spec,CP position. do is also in C, it was moved from I to form the question (auxiliary inversion).
This sentence contains three CPs:
*[CP lies[CP [C do [IP you [VP think [CP [C that [VP she [V tells[VP you [V t [DP {moved lies}]]]]]]]]]]]]
This is an example of object topicalization in English. The second NP object lies of the verb tell was extracted (moved) from an embedded position into the highest Spec,CP position (remember scope over clause I explained the other day).
The first CP, i.e., [CP lies.., is a topic projection, its specifier is occupied only by topicalized elements, not wh-moved elements. This is why we need a second CP, i.e., [CP [C do.., to provide a position of the moved auxiliary to form a question (auxiliary inversion). The third CP is the intermediate CP that is headed by the relative complementizer that. This CP provides Spec,CP as an embedded position for movement to rest it.
Now, this movement is ungrammatical, hence the ungrammaticality of the sentence. But why?
Topicalised objects are expected to have scope over the CP, in this case there're more than one. It cannot have scope over all the three CPs. The argument for this claim is a sentence where we remove these additional CPs, and get a grammatical version:
Lies, she tell you.