Как сохранить в переменную и отобразить в lineEdit?

Не изменяйте код, сгенерированный Qt Designer. Создайте другой класс, который наследуется от соответствующего виджета, и используйте созданный класс для его заполнения.

Сделать вызов метода self.generate_password() и свставить несколько проверок.

from PyQt5 import QtCore, QtGui, QtWidgets
import random


class Ui_Dialog(object):
    def setupUi(self, Dialog):
        Dialog.setObjectName("Dialog")
        Dialog.resize(318, 114)
        self.verticalLayout = QtWidgets.QVBoxLayout(Dialog)
        self.verticalLayout.setObjectName("verticalLayout")
        self.lineEdit = QtWidgets.QLineEdit(Dialog)
        self.lineEdit.setObjectName("lineEdit")
        self.verticalLayout.addWidget(self.lineEdit)
        self.horizontalLayout = QtWidgets.QHBoxLayout()
        self.horizontalLayout.setObjectName("horizontalLayout")
        self.label = QtWidgets.QLabel(Dialog)
        self.label.setObjectName("label")
        self.horizontalLayout.addWidget(self.label)
        self.lineEdit_2 = QtWidgets.QLineEdit(Dialog)
        sizePolicy = QtWidgets.QSizePolicy(QtWidgets.QSizePolicy.Expanding, QtWidgets.QSizePolicy.Fixed)
        sizePolicy.setHorizontalStretch(0)
        sizePolicy.setVerticalStretch(0)
        sizePolicy.setHeightForWidth(self.lineEdit_2.sizePolicy().hasHeightForWidth())
        self.lineEdit_2.setSizePolicy(sizePolicy)
        self.lineEdit_2.setMaximumSize(QtCore.QSize(16777215, 16777215))
        self.lineEdit_2.setObjectName("lineEdit_2")
        self.horizontalLayout.addWidget(self.lineEdit_2)
        spacerItem = QtWidgets.QSpacerItem(40, 20, QtWidgets.QSizePolicy.Expanding, QtWidgets.QSizePolicy.Minimum)
        self.horizontalLayout.addItem(spacerItem)
        self.checkBox = QtWidgets.QCheckBox(Dialog)
        self.checkBox.setObjectName("checkBox")
        self.horizontalLayout.addWidget(self.checkBox)
        self.verticalLayout.addLayout(self.horizontalLayout)
        self.pushButton = QtWidgets.QPushButton(Dialog)
        self.pushButton.setObjectName("pushButton")
        self.verticalLayout.addWidget(self.pushButton)

        self.retranslateUi(Dialog)
        QtCore.QMetaObject.connectSlotsByName(Dialog)

    def retranslateUi(self, Dialog):
        _translate = QtCore.QCoreApplication.translate
        Dialog.setWindowTitle(_translate("Dialog", "Dialog"))
        self.label.setText(_translate("Dialog", "Длина пароля:"))
        self.checkBox.setText(_translate("Dialog", "Сохранить в .txt"))
        self.pushButton.setText(_translate("Dialog", "СГЕНЕРИРОВАТЬ ПАРОЛЬ"))


class Dialog(QtWidgets.QDialog, Ui_Dialog):
    def __init__(self):
        super().__init__()    
        self.setupUi(self)

        self.password = ''
        
        #self.checkBox.stateChanged.connect(self.event_password)
        self.pushButton.clicked.connect(self.display_and_save_password)

    def generate_password(self):
        upper = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
        lower = 'abcdefghijklmnopqrstuvwxyz'
        numbers = '0123456789'
        symbols = '[]{}()*;/,._-'
        all = lower + upper + numbers + symbols
        length = int(self.lineEdit_2.text())
        self.password = ''.join(random.sample(all, length))
        print(self.password)

    def save_in_file(self): 
        with open ('password.txt', 'w') as file:
            file.write(self.password)

    def display_and_save_password(self):
        if not self.lineEdit_2.text():
            msg = QtWidgets.QMessageBox.information(self, 
                'Внимание', 'Укажите длину пароля.')
            return
        
        self.generate_password()                                           # +++
    
        self.lineEdit.setText(self.password)
        
        if self.checkBox.isChecked():                                       # +++
            save_password = self.save_in_file()
            msg = QtWidgets.QMessageBox.information(self, 
                    'Успех', 'Пароль сохранен в .txt.')

if __name__ == "__main__":
    import sys
    app = QtWidgets.QApplication(sys.argv)
    w = Dialog()
    w.show()
    sys.exit(app.exec_())