### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

`latency-based-routing` degrades to random selection weighted by deployment count when handling concurrent requests. With 16 Anthropic keys + 4 OpenAI keys per tier, traffic distributes 80/20 matching the key ratio regardless of actual latency differences between providers (e.g., OpenAI GPT-4.1 at ~583ms vs Anthropic Claude Sonnet at ~1,588ms).

**Expected:** Router should favor the faster provider. **Actual:** Traffic distributes proportionally to deployment count — identical to `simple-shuffle`.

**Root cause:** `async_log_success_event()` in `litellm/router_strategy/lowest_latency.py` performs a non-atomic read-modify-write on a shared cache key (`{model_group}_map`). When concurrent requests complete simultaneously, the last writer overwrites all previous updates, causing latency data to be constantly lost. Deployments with lost data fall back to `latency: [0]` (treated as fastest) and are randomly selected, producing a distribution proportional to deployment count.

```python # READ — no lock request_count_dict = await self.router_cache.as…