Why isn't a defendant entitled to an attorney if a lineup is conducted before the person is arrested?
The defendant is entitled to an attorney at any time. However, if the lineup is conducted before the person is arrested, they will not have been read their Maranda Rights. The person will not need an attorney. The court is not necessarily obligated to provide an attorney until an arrest has been made. It is important for a person to have an attorney during a lineup even if it is conducted after an arrest but before the person is formally charged. Procedural mistakes or other mistakes could easily occur during a lineup. If the defendant does not have an attorney, these mistakes might not be avoided or remedied. In the link below, you can find more information on this topic; you may want to check out the section titled "Lineups and Other Identification Situations."
Simply put, if you are not yet charged, or more properly put,not yet arrested, then your 6th Amendment rights do not apply. It is only after you've been charged that your right to counsel kicks in. Indeed,if I correctly understand your premise, then the person in the line-up is not under arrest, and is free to refuse to take part in the line-up. He may leave.
If he is in fact under arrest, then he should be represented by counsel at any line-up. Failure to honor that right will almost certainly result in the line-up results being suppressed.
One last note: Miranda is not required if the person is not in custody.