This largely depends on your installation. For accounts using the asynchronous tag, our default and recommended approach, Lytics will never affect page load times. All of our processing and collection is done in the background while your website loads normally.
For those using the (now unsupported) synchronous tag, it is possible for Lytics to affect load times. However, our services will timeout after two seconds and fail gracefully so there is little chance of a prolonged delay in loading due to Lytics related code or services. Proper defaults or fallbacks should be put in place to handle the absence of data returned from Lytics in those instances.