(f)lock during uv run (#14153)

This is very similar to the locking added for `uv sync`, `uv add`, and
`uv remove` in https://github.com/astral-sh/uv/pull/13869. Improving our
(f)locking in general is tracked in
https://github.com/astral-sh/uv/issues/13883.

crates/uv/src/commands/project/run.rs

@@ -240,6 +240,8 @@ hint: If you are running a script with `{}` in the shebang, you may need to incl
             .await?
             .into_environment()?;
 
+            let _lock = environment.lock().await?;
+
             // Determine the lock mode.
             let mode = if frozen {
                 LockMode::Frozen
@@ -382,6 +384,8 @@ hint: If you are running a script with `{}` in the shebang, you may need to incl
                         )
                     });
 
+                let _lock = environment.lock().await?;
+
                 match update_environment(
                     environment,
                     spec,
@@ -694,6 +698,8 @@ hint: If you are running a script with `{}` in the shebang, you may need to incl
                         .map(|lock| (lock, project.workspace().install_path().to_owned()));
                 }
             } else {
+                let _lock = venv.lock().await?;
+
                 // Determine the lock mode.
                 let mode = if frozen {
                     LockMode::Frozen