下面是一个简单的示例，展示了如何在Android Room SQLite中使用自定义查询与MVVM模式。

首先，在build.gradle文件中添加以下依赖项：

implementation 'androidx.room:room-runtime:2.3.0'
kapt 'androidx.room:room-compiler:2.3.0'

接下来，创建一个实体类（Entity）：

@Entity(tableName = "users")
data class User(
    @PrimaryKey val id: Int,
    val name: String,
    val age: Int
)

然后，创建一个数据访问对象（DAO）：

@Dao
interface UserDao {
    @Query("SELECT * FROM users")
    fun getAllUsers(): LiveData>

    @Query("SELECT * FROM users WHERE age > :minAge")
    fun getUsersByAge(minAge: Int): LiveData>

    @Insert(onConflict = OnConflictStrategy.REPLACE)
    suspend fun insertUser(user: User)

    @Delete
    suspend fun deleteUser(user: User)
}

接下来，创建一个数据库类：

@Database(entities = [User::class], version = 1)
abstract class AppDatabase : RoomDatabase() {
    abstract fun userDao(): UserDao

    companion object {
        @Volatile
        private var INSTANCE: AppDatabase? = null

        fun getDatabase(context: Context): AppDatabase {
            return INSTANCE ?: synchronized(this) {
                val instance = Room.databaseBuilder(
                    context.applicationContext,
                    AppDatabase::class.java,
                    "app_database"
                ).build()
                INSTANCE = instance
                instance
            }
        }
    }
}

然后，创建一个仓库类：

class UserRepository(private val userDao: UserDao) {
    val allUsers: LiveData> = userDao.getAllUsers()

    fun getUsersByAge(minAge: Int): LiveData> {
        return userDao.getUsersByAge(minAge)
    }

    suspend fun insertUser(user: User) {
        userDao.insertUser(user)
    }

    suspend fun deleteUser(user: User) {
        userDao.deleteUser(user)
    }
}

接下来，创建一个ViewModel类：

class UserViewModel(private val userRepository: UserRepository) : ViewModel() {
    val allUsers: LiveData> = userRepository.allUsers

    fun getUsersByAge(minAge: Int): LiveData> {
        return userRepository.getUsersByAge(minAge)
    }

    fun insertUser(user: User) {
        viewModelScope.launch(Dispatchers.IO) {
            userRepository.insertUser(user)
        }
    }

    fun deleteUser(user: User) {
        viewModelScope.launch(Dispatchers.IO) {
            userRepository.deleteUser(user)
        }
    }
}

最后，在Activity或Fragment中使用ViewModel来获取和操作数据：

class MainActivity : AppCompatActivity() {
    private lateinit var userViewModel: UserViewModel

    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        setContentView(R.layout.activity_main)

        val userDao = AppDatabase.getDatabase(application).userDao()
        val userRepository = UserRepository(userDao)
        userViewModel = ViewModelProvider(this, UserViewModelFactory(userRepository)).get(UserViewModel::class.java)

        // 获取所有用户
        userViewModel.allUsers.observe(this, { users ->
            // 更新UI
        })

        // 获取年龄大于20的用户
        userViewModel.getUsersByAge(20).observe(this, { users ->
            // 更新UI
        })

        // 插入新用户
        val newUser = User(1, "John Doe", 25)
        userViewModel.insertUser(newUser)

        // 删除用户
        userViewModel.deleteUser(newUser)
    }
}

这就是一个简单的使用Android Room SQLite进行自定义查询与MVVM的示例。你可以根据自己的需求进行修改和扩展。