Gamma-ray bursts are immense flashes of high-energy radiation originating from stellar death processes in distant galaxies. Many bursts exhibit a time delay between the high- and low-energy components of their emission, known as the spectral lag. For the class of long gamma-ray bursts, there is a known relationship between the spectral lag and the peak luminosity of the burst, which can otherwise be difficult to determine. The spectral lag is generally measured through cross-correlation analysis of the entire GRB light curve, but many bursts have a complex temporal structure which may include distinct sub-events of varying intensity. We present a time-resolved cross-correlation method for investigating the lag-luminosity correlation between slices of gamma-ray bursts, and apply this method to a sample of long GRBs detected by the BATSE gamma-ray observatory. The analysis produces a lag-luminosity correlation parameter for each burst in the sample, and we discuss the statistical behavior of these results. In particular, we consider the extent to which the whole-burst lag-luminosity correlation extends to these intra-burst measurements.