I've gone over the documentation and cannot find a clear statement regarding how much latency is X-ray tracing supposed to add to Lambda function executions (and to other services as well). It should be minimal, but since it's sending out traces, some latency is expected.
Does anyone have the numbers?
AWS X-Ray SDKs which you use in your application do not send trace segments to X-Ray service directly. The segments are transmitted over UDP to xray daemon running on localhost. So the latency involved is only for in memory updates to the segment data. Only when the segments are complete, they are sent over UDP to localhost. Hence, you should expect minimal possible overhead on your application. Also the daemon which runs in a separate process does not send segments to the service immediately. It buffers the segments for a short period and periodically sends them in batches using the PutTraceSegments API call.
If you are interested to dig further, most AWS X-Ray SDKs are open sourced on GitHub. Java SDK for example https://github.com/aws/aws-xray-sdk-java