Как сделать чтобы при нажатии на кнопку бралось число из lineEdit и подставлялось в функцию расчёта и рисования QPainter используя flag и update()?

Попробуйте так:

import sys
# ???import PyQt5
from PyQt5 import QtCore, QtWidgets
from PyQt5.Qt import *


class Ui_MainWindow(object):
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(614, 478)
        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setObjectName("centralwidget")
        self.gridLayout = QtWidgets.QGridLayout(self.centralwidget)
        self.gridLayout.setObjectName("gridLayout")
        self.tabWidget = QtWidgets.QTabWidget(self.centralwidget)
        self.tabWidget.setObjectName("tabWidget")
        
        #self.tab = QtWidgets.QWidget()
        self.tab = Tab_1Widget()
        
        self.tab.setObjectName("tab")
        self.lineEdit = QtWidgets.QLineEdit(self.tab)
        self.lineEdit.setGeometry(QtCore.QRect(40, 70, 113, 20))
        self.lineEdit.setObjectName("lineEdit")
        self.pushButton = QtWidgets.QPushButton(self.tab)
        self.pushButton.setGeometry(QtCore.QRect(180, 70, 75, 23))
        self.pushButton.setObjectName("pushButton")
        self.tabWidget.addTab(self.tab, "")
        
#        self.tab_2 = QtWidgets.QWidget()
        self.tab_2 = Tab_2Widget()                                  # +++
        self.tab_2.setObjectName("tab_2")
        
        self.pushButton_2 = QtWidgets.QPushButton(self.tab_2)
        self.pushButton_2.setGeometry(QtCore.QRect(480, 90, 75, 23))
        self.pushButton_2.setObjectName("pushButton_2")
        self.lineEdit_2 = QtWidgets.QLineEdit(self.tab_2)
        self.lineEdit_2.setGeometry(QtCore.QRect(340, 90, 113, 20))
        self.lineEdit_2.setObjectName("lineEdit_2")
        self.tabWidget.addTab(self.tab_2, "")
        
        self.gridLayout.addWidget(self.tabWidget, 0, 0, 1, 1)
        MainWindow.setCentralWidget(self.centralwidget)
        self.statusbar = QtWidgets.QStatusBar(MainWindow)
        self.statusbar.setObjectName("statusbar")
        MainWindow.setStatusBar(self.statusbar)

        self.retranslateUi(MainWindow)
        self.tabWidget.setCurrentIndex(0)
        QtCore.QMetaObject.connectSlotsByName(MainWindow)

    def retranslateUi(self, MainWindow):
        _translate = QtCore.QCoreApplication.translate
        MainWindow.setWindowTitle(_translate("MainWindow", "MainWindow"))
        self.pushButton.setText(_translate("MainWindow", "PushButton"))
        self.tabWidget.setTabText(self.tabWidget.indexOf(self.tab), _translate("MainWindow", "Tab 1"))
        self.pushButton_2.setText(_translate("MainWindow", "PushButton"))
        self.tabWidget.setTabText(self.tabWidget.indexOf(self.tab_2), _translate("MainWindow", "Tab 2"))


class Tab_1Widget(QtWidgets.QWidget):
    def __init__(self):
        super().__init__()
        
        self.flag = False
        self.c = 0                                                   # +++

    def paintEvent(self, e):
        if self.flag:
            qp = QPainter()
            qp.begin(self)
            self.drawRectangles(qp)
            qp.end()

    def drawRectangles(self, qp):
        qp.drawRect(10, 150, self.c, 60)

        
class Tab_2Widget(QtWidgets.QWidget):
    def __init__(self):
        super().__init__()
        
        self.flag = False
        self.c = 0                                                   # +++

    def paintEvent(self, e):
        if self.flag:
            qp = QPainter()
            qp.begin(self)
            self.drawRectangles(qp)
            qp.end()

    def drawRectangles(self, qp):
        qp.drawRect(10, 150, 150, self.c)


class Example(QtWidgets.QMainWindow, Ui_MainWindow):
    def __init__(self):
        super().__init__()
        self.setupUi(self)
        
        self.pushButton.clicked.connect(self.onClicked)
        self.pushButton_2.clicked.connect(self.onClicked2)

    def onClicked(self):
        self.tab.flag = True
# +++ vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
        try:
            a = int(self.lineEdit.text())
        except:
            a = 0
        b = a * 2
        c = a + b        
        self.tab.c = a + b
# +++ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
        self.update()

    def onClicked2(self):
        self.tab_2.flag = True
# +++ vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
        try:
            a = int(self.lineEdit_2.text())
        except:
            a = 0

        b = a + 20  
        
# ???   self.tab_2.c = b - a 
        self.tab_2.c = b - a / 2
        
# ???   self.lineEdit_2.setText(f'{self.tab_2.c}')
# +++ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
     
        self.update()
        
        

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