Do I need to lock singleton in ASP.NET Core?

Here is my code:

public class RouteSingleton
{
    private IDictionary<string, string> _dealCatLinks;
    private IDictionary<string, string> _sectionLinks;
    private IDictionary<string, string> _categoryLinks;
    private IDictionary<string, string> _materials;
    private IDictionary<string, string> _vendors;
    public RouteSingleton(IDealService dealService
        , ICategoryService categoryService
        , IVendorService vendorService)
    {


        this._dealCatLinks = dealService.GetDealCatLinks("PLV").Distinct().ToDictionary(x => x, x => x);
        this._sectionLinks = categoryService.GetSectionLinks("PLV").Distinct().ToDictionary(x => x, x => x);
        this._categoryLinks = categoryService.GetMainCategoryLinks("PLV")
            .Where(x => !_sectionLinks.ContainsKey(x)).Distinct().ToDictionary(x => x, x => x);
        this._vendors = _vendorService.GetVendorLinks("PFB").Distinct().ToDictionary(x => x, x => x);

    }

    public bool IsDealCategory(string slug)
    {
        return _dealCatLinks.ContainsKey(slug);
    }

    public bool IsSectionUrl(string slug)
    {
        return _sectionLinks.ContainsKey(slug);
    }

    public bool IsCategory(string slug)
    {
        return _categoryLinks.ContainsKey(slug);
    }       

    public bool IsVendor(string slug)
    {
        return _vendors.ContainsKey(slug);
    }
}

Here is how I register in startup.cs:

services.AddSingleton<RouteSingleton, RouteSingleton>();

And I use the singleton in route constraints like so:

routes.MapRoute("category", "{slug}", defaults: new { controller = "Category", action = "Index" }, constraints: new { slug = new CategoryConstraint(app.ApplicationServices.GetRequiredService<RouteSingleton>()) });

1. I wonder do I need to lock threads in my RouteSingleton.cs or my code will work fine under lots of users on application start?
2. If I need to lock what way you can suggest to me?
3. What will happen if I don't?