Praise be to Allah.
Firstly: It should be noted that making vows is makrooh, because of the marfoo’ hadeeth of Abu Hurayrah (may Allaah be pleased with him): “Do not make vows, for vows do not affect the divine will at all, all they do is get something from a stingy person.” Narrated by al-Bukhaari, 6609; Muslim, 1640. This version narrated by Muslim.
And it was narrated from Ibn ‘Umar (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) forbade vows and said that they do not do any good, rather they just get something from a stingy person. Narrated by Muslim, 1639. A person may oblige himself to do something by making a vow then not fulfil it, thus he puts pressure on himself and exposes himself to sin.
Being negligent with regard to a vow is a serious matter, and there is the fear that the one who does that is included in the verses in which Allaah says (interpretation of the meaning):
“And of them are some who made a covenant with Allaah (saying): “If He bestowed on us of His Bounty, we will verily, give Sadaqah (Zakaah and voluntary charity in Allaah’s Cause) and will be certainly among those who are righteous.”
76. Then when He gave them of His Bounty, they became niggardly [refused to pay the Sadaqah (Zakaah or voluntary charity)], and turned away, averse.
77. So He punished them by putting hypocrisy into their hearts till the Day whereon they shall meet Him, because they broke that (covenant with Allaah) which they had promised to Him and because they used to tell lies”
Concerning the seriousness of being negligent with regard to vows, see also question no. 42178.
With answer to this particular question, the vow which you made is a vow of obligation, i.e., it is obligatory for you to fulfil it, because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever vows to obey Allaah, let him obey Him, and whoever vows to disobey Allaah, let him not disobey Him.” Narrated by al-Bukhaari, 6696.
Based on this, you have to fulfil your vow. With regard to the days when you did not fast, you have to make them up. As well as that you have to offer kafaarat yameen (expiation for breaking a vow). One expiation is sufficient for all the days when you did not fast.
Ibn Qudaamah was asked in al-Mughni (13/648) about a person who vowed to fast every Thursday forever, then he did not fast for several days. He said; Let him make up his vow and offer expiation… If he has missed many days, then he has to offer one expiation for all of them. If he offered expiation then he missed some more days, then he has to offer another expiation. This was stated by Ahmad.
Your being invited to lunch is not regarded as an excuse that allows you not to fast and not to fulfil the vow. You can tell them about your vow so that you will have an excuse not to attend. And Allaah knows best.