After a suitable IPTG induction period, I generally spin down my culture at 8000 rpm for 10 mins at 4C and then save the bacterial pellet. This pellet can be stored in a -20C freezer for several months. I have sometimes stored my pellets in a -80C deep freezer for up to a year.
You can store your IPTG-induced cell pellets at -20 degrees and even at -80 degrees for several months. Your proteins would remain intact. However, it is not advisable (ideally) to perform experiments with cell pellets that have been stored for long at sub-zero temperatures. There are very low, but fair chances of ending up with some cellular artifacts and unwarranted false (+) ve or (-) ve results.
You can also quickly freeze the lysed cells in liquid nitrogen and store them at -80°C. Remember to add PMSF and TCEP when lysing the sample to prevent the protein from oxidation and inhibit protein degradation. Thaw the sample slowly and avoid repeated freezing and thawing.