If the lag is caused by an army being "teleported" into trapped territory after a peace treaty, granting that faction 5 turns of Military Access can allow them to move out and clear the hang-up.

This is the most reliable "passive" fix. Park a single ship in the strait between Istanbul and Anatolia. This forces the AI to stop trying to pathfind across the land bridge, often instantly ending the lag.

In the modern era, further hardware solutions have emerged. As Empire: Total War is an older title, it relies heavily on single-core CPU performance. Modern overclocking and the use of "Large Address Aware" (LAA) patches—which allow the 32-bit application to utilize more than 2GB of RAM—have further mitigated the issue. When combined with a total conversion mod and modern hardware, the infamous Ottoman lag is effectively neutralized.