Was Judas the traitor present when the Lord shared with the disciples the institution of the Lord's Supper ? The answer is no, by that time he [judas] had left to go make arrangements to be tray his Master Many think because of Lk 22:21
21 But, behold, the hand of him that betrayeth me is with me on the table.
The key here is the word's "on the table", the passover table is meant !
This coincides with Matt 26:21
21 But, behold, the hand of him that betrayeth me is with me on the table.
However this does not mean that judas was with them when the Lord's Supper commenced after the Passover !
This begins with them all celebrating the passover meal, a Jewish holiday, and it was a meal that judas, being a physical descendant of the Abraham, and his ancestors that took part of the original passover in Exodus 12, of which many of whom were not even believers, for most of them perished in the wilderness , as it is written Heb 3:7-12;4:1-6
Now we know that this [the passover meal or table] is that which judas shared in by comments Matt 26:23
23 And he answered and said, He that dippeth his hand with me in the dish, the same shall betray me.
Passover dish !
Jn 13:26
26 Jesus answered, He it is, to whom I shall give a sop, when I have dipped it. And when he had dipped the sop, he gave it to Judas Iscariot, the son of Simon.
The custom of the passover meal was to take a piece of meat or bread and dip it into a common bowl of sauce on the Table !
Again this was a already existing custom for the historical passover meal celebration, which judas had a right to as a physical jew ! But the commencement of the Lords supper had not yet began !
Now the record shows that after judas took the sop, he said " is it i rabbi ? Jesus replied, thou hast said ! Matt 26:25
25 Then Judas, which betrayed him, answered and said, Master, is it I? He said unto him, Thou hast said.
Now at this very same point in time in John's account it reads Jn 13:26-27,30
26 Jesus answered, He it is, to whom I shall give a sop, when I have dipped it. And when he had dipped the sop, he gave it to Judas Iscariot, the son of Simon.
27 And after the sop Satan entered into him. Then said Jesus unto him, That thou doest, do quickly.
And vs 30 confirms that judas departed immediately after the sop Vs 30
30 He then having received the sop went immediately out: and it was night.
This time coincides with Matt 26:25
25 Then Judas, which betrayed him, answered and said, Master, is it I? He said unto him, Thou hast said.
And it was afterwards, after the sop of passover, and he left into the night, that the Lords Supper began Vs 26
26 And as they were eating, Jesus took bread, and blessed it, and brake it, and gave it to the disciples, and said, Take, eat; this is my body.
27 And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it;
28 For this is my blood of the new testament, which is shed for many for the remission of sins.
29 But I say unto you, I will not drink henceforth of this fruit of the vine, until that day when I drink it new with you in my Father's kingdom.
30 And when they had sung an hymn, they went out into the mount of Olives.
However at this point judas had left into the night !