Unfortunately, the lien remains (even if all the taxes were discharged) and a tax lien is not avoidable (as in the case of involuntary judgment liens). However, the lien will likely NOT attach to property acquired post-petition because that would be tantamount to attempting to collect a discharged debt in violation of the discharge injunction.
If the taxes were a lien before the filing of the Chapter 7 then the lien is not discarged so that will remain a lien against any property post petition. If the taxes were priority non-discarged then they can still attache to post peition property. You may want to consider a Chapter 13 to repay any nondiscarged or secured tax liability over time.
The first question that comes to my mind after reading your question is - how can you be sure the taxes were in fact discharged in the bankruptcy proceeding? Tax debts do not get discharged just because they are listed in the bankruptcy. They are very difficult to discharge unless very specific criteria is satisfied concerning the tax year involved, the date the tax return was filed, the date the tax was assessed, whether there have been any "tolling" events, such as a pending offer in compromise, and many other factors. If in fact the taxes were dischargeable, then a separate motion should have been filed to avoid and remove the tax lien. Fo you to have supposedly "discharged" tax debt, but an IRS lien that remains, makes me think that maybe the tax debt hasn't actually been discharged. Have you called the IRS Insolvency section to inquire as to the status of the discharge?
If somehow the tax debt has gone away, and you did not get the tax lien removed, then I believe it will remain in place as a lien against any & all of your property, whether pre- or post-petition property. However, normally any lien that is associated with discharged tax debt will automatically be removed by the IRS. In other words, if they are in agreement that the underlying tax is dischargeable and in fact has been discharged, then any lien that relates to those discharged taxes will be removed. If this is your situation, but they haven't removed the lien, then call the IRS Insolvency section and request they remove their lien.
Unfortunately, however, my guess is that when you call you will find out that the lien remains because the tax debt has not in fact been discharged.