Balance two different HttpClients without impacting throughput - asp.net-core

Question

I have the following controller
[Route("some-value")]
[ApiController]
public class SomeValueController : ControllerBase
{
private readonly ClientProvider _clientProvider;
public SomeValueController(ClientProvider clientProvider)
{
_clientProvider = clientProvider;
}
[HttpGet]
public async Task<ActionResult> Index([FromQuery] string from, [FromQuery] string to)
{
var values = await _clientProvider.GetClient().GetValues(from, to);
return Ok(values);
}
}
I want this controller to use one HttpClient for 50% of requests and a different HttpClient for the other 50% of requests. That's why i have introduced the ClientProvider. It is currently implemented as follows:
public class ClientProvider
{
private readonly MainClient _mainClient;
private readonly BackupClient _backupClient;
private readonly ILogger<ClientProvider> _logger;
private bool _flag = false;
private object _lock = new Object();
public ClientProvider(BackupClient backupClient,
MainClient mainClient, ILogger<ClientProvider> logger)
{
_backupClient = backupClient;
_mainClient = mainClient;
_logger = logger;
}
public IExchangeClient GetClient()
{
lock (_lock)
{
var client = _flag ? _backupClient as IExchangeClient : _mainClient;
_flag = !_flag;
return client;
}
}
}
It is obviously very naive because it will block for some time when the appropriate client is being selected. The lock is required for situations in which requests arrive almost simultanously. If the lock wasn't there i would have the same client selected for all those simultanous requests because they would all execute the same line at the same time in separate threads. Can this problem be solved in a more elegant and efficient way?