手順

ViewComposerを導入する
「adminlte::partials.sidebar.menu-item」で使用するviewcomposer「SidebarMenuItemComposer」を作成する
$item['class']に「active」が追加されるようにする
「SidebarMenuItemComposer」を「adminlte::partials.sidebar.menu-item」に関連付ける

以下コード

/app/Http/ViewComposers/SidebarMenuItemComposer.php

<?php

namespace App\Http\ViewComposers\User\Worker;

use Auth;
use Illuminate\View\View;

/**
 * Class ModalSearchCemeteryComposer
 * @package App\Http\ViewComposers\User\Worker
 */
class SidebarMenuItemComposer
{
    /**
     * @param View $view
     */
    public function compose(View $view)
    {
        // 現在のページに応じて左メニューをactiveにする
        $path = request()->path();
        $host = request()->getHttpHost();
        $http = $this->isSsl() ? 'https' : 'http';

        $item = $view->getData('item'); 
        $pattern = str_replace($http.'://'.$host.'/', '', $item['item']['href']);
        if (!$item['item']['active'] && ($pattern === $path || strpos($path, $pattern.'/') === 0)) {
            $item['item']['class'] .= ' active ';
        }
        $view->with(['item' => $item['item']]);
    }

    //Webサーバー毎にキーと値で判別
    private function isSsl()
    {
        if (isset($_SERVER['HTTPS']) === true ) // Apache
        {
            return ($_SERVER['HTTPS'] === 'on' or $_SERVER['HTTPS'] === '1' );
        }
        elseif (isset($_SERVER['SSL']) === true ) // IIS
        {
            return ($_SERVER['SSL'] === 'on' );
        }
        elseif (isset($_SERVER['HTTP_X_FORWARDED_PROTO']) === true ) // Reverse proxy
        {
            return (strtolower($_SERVER['HTTP_X_FORWARDED_PROTO']) === 'https' );
        }
        elseif (isset($_SERVER['HTTP_X_FORWARDED_PORT']) === true ) // Reverse proxy
        {
            return ($_SERVER['HTTP_X_FORWARDED_PORT'] === '443' );
        }
        elseif (isset($_SERVER['SERVER_PORT']) === true )
        {
            return ($_SERVER['SERVER_PORT'] === '443' );
        }

        return false;
    }
}

/app/Providers/ViewComposerServiceProvider.php


<?php

namespace App\Providers;

use Illuminate\Support\ServiceProvider;
use View;

class ViewComposerServiceProvider extends ServiceProvider
{
    /**
     * Register services.
     *
     * @return void
     */
    public function register()
    {
        //
    }

    /**
     * Bootstrap services.
     *
     * @return void
     */
    public function boot()
    {
        View::composers([
            \App\Http\ViewComposers\User\Worker\SidebarMenuItemComposer::class => 'adminlte::partials.sidebar.menu-item',
        ]);
    }
}