Must you be self-controlled to eat the Lord’s Supper, or does eating the Lord’s Supper help you be self-controlled? Is it requirement or result? Self-control and communion aren’t always connected, but they can’t help it.
Self-control does matter when it comes to those invited to the Table, and in a couple ways.
There is a kind of self-control that is driven by the flesh, that follows worldly standards, and that tries to earn righteousness. Asceticism comes to mind (Colossians 2:16-23). You cannot depend on yourself to make yourself worthy, the worthy eat and drink by faith.
And it is possible to meet as believers in the name of Jesus and still be selfish, serving oneself, and so failing to demonstrate the fruit of love in self-control. This was the problem Paul addressed in 1 Corinthians 11, and those who failed to properly judge themselves, i.e., show self-control, were not worthy to participate.
For that matter, ignoring God’s Word and choosing any sin over sanctification, rationalizing your fleshly wants over His will, should convict you to get right with Christ, not act like you are in fellowship.
Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord. (1 Corinthians 11:27)
Those who come to the Supper by faith, who are in fellowship with Christ, are strengthened in faith and in fellowship such that advances in self-control do follow from communion.