TypeError: list indices must be integers or slices, not Button Tkinter

Here’s a version of your code with a number of changes. It fixes the TypeError and gets rid of the card_dict. Its not really needed anyway because that number assigned to each card can easily be stored by adding an attribute to the Button widget representing the card. Doing this also means you only have to pass the card to the WrongOrRight() function.

All important changes have been indicated with # ALL CAPS COMMENTS. I also made cosmetic changes to the code so it followed the PEP 8 – Style Guide for Python Code in an effort to make it more readable and I strongly suggest that you read and follow the guidelines in the future yourself.

from tkinter import *
from tkinter import messagebox
import time
import random

difficulty = 16
rowsize= 4
columnsize = 4
numcount = 0
lastnum = 0
gotitcorrect = False

root = Tk()
root.title("MEMORY GAME!!")
root.configure(bg='gray')

def GameStart():
    menuFrame.pack_forget()
    gameFrame.pack()

def Timer(tim):
    time.sleep(tim)

def GetRandomNumber():
    lst1 = [i for i in range(1,9)]
    lst2 = [i for i in range(1,9)]
    random.shuffle(lst1), random.shuffle(lst2)
    numlst = lst1+lst2
    return numlst

def WrongOrRight(card): # REMOVED NO LONGER NEEDED SECOND ARGUMENT.
    global lastnum, numcount, gotitcorrect  # ADDED

    number = card.number  # ADDED
    if numcount == 0:
        lastnum = number
        numcount += 1
        card.configure(text=str(number))
    elif numcount == 1:
        if number == lastnum:
            gotitcorrect = True
            card.configure(text=str(number))
        else:
            gotitcorrect = False
            card.configure(text='')
        numcount -= 1

menuFrame = Frame(root, bg='gray')
menu = [Label(menuFrame, text='MEMORY GAME', bg='gray'),
        Button(menuFrame, command=GameStart, text='Start', bg='gray')]
for i in menu:
    i.pack()
menuFrame.pack()

numlst = GetRandomNumber()
print(numlst)
gameFrame = Frame(root, bg='gray')
cards = [[Button(gameFrame) for j in range(4)] for i in range(4)]
index = 1
#card_dict = {}  # NOT NEEDED
for x in range(rowsize):
    for y in range(columnsize):
        print(index)
        cards[x][y].grid(row=y, column=x, padx=20, pady=20)
        cards[x][y].configure(text=str(numlst[index-1]))
        # ADDED DEFAULT ARGUMENTS TO LAMBDA FUNCTION TO MAKE IT WORK PROPERLY
        cards[x][y].configure(command=lambda x=x, y=y: WrongOrRight(cards[x][y]))
        cards[x][y].number = numlst[index-1]  # ADD ATTRIBUTE TO BUTTON WIDGET
#        card_dict[cards[x][y]] = numlst[index-1]  # NOT NEEDED
        index += 1

#Timer(5)  # DISABLED FOR TESTING
for x in range(rowsize):
    for y in range(columnsize):
        cards[x][y].configure(text='')

root.grid_rowconfigure(0,weight=1)
root.grid_columnconfigure(0,weight=1)
root.grid_rowconfigure(rowsize,weight=1)
root.grid_columnconfigure(columnsize,weight=1)

root.mainloop()