Thanks for your question.
On the face of it what did the vow entail?
1. Judges 11:29 When he made his vow, the Holy Spirit, which leads to all truth and into trial, had come upon him (cp. John 16:13; and Matthew 4:1). Romans 12:1 Jephthah would hold nothing back from God. Was the vow then well thought out or was it rash? Was it necessary?
Ecclesiastes 5:2 Be not rash with your mouth, nor let your heart be hasty to utter a word before God, for God is in heaven, and you upon earth; therefore let your words be few.
2. Hebrews 11:32 Jephthah is listed in the honour roll of the faithful. If he had offered his daughter as a human sacrifice, he would have violated a fundamental principle of the Law - see Deut. 18:9,10 and Jer. 7:31 (see margin). Human sacrifice was an utter abomination to God. Clearly, Jephthah did not offer his daughter as a burnt offering nor did the law require it.
3. The vow is in 2 parts joined by the Hebrew word "vav" which means "and." Jephthah actually said, "Whoever comes forth of the doors of my house to meet me, when I return in peace from the children of Ammon, shall surely be the LORD’S, and I will offer it up for a burnt offering." The last part in the Hebrew should read, "...and I will offer up to Him a burnt offering." This is exactly what happened when Samuel was offered in service for life at the Tabernacle. Hannah brought Samuel to offer him to the LORD and she brought bullocks for a burnt offering.
4. See 1 Samuel 1:25-28 And they slew a bullock, and brought the child to Eli. And she said, Oh my lord, as thy soul liveth, my lord, I am the woman that stood by thee here, praying unto the LORD. For this child I prayed; and the LORD hath given me my petition which I asked of him: Therefore also I have lent him to the LORD; as long as he liveth he shall be lent to the LORD.
5. He vowed that whoever - not whatever (he wouldn't expect an animal to come out of his house to greet him) - first came out of his house to greet him after his victory would be given in service to the LORD for life and he would offer up burnt offerings - just like Hannah did later with Samuel. He was shocked that it was his daughter and not his servant.
6. Note that Exodus 38:8; 1 Samuel 2:22 describes the role of women who served at the Tabernacle. Also, consider the case of Anna in Luke 2:36,37
7. The word "lament" in verse 40 is better translated "celebrate" or "praise" and the R.V. margin has "talk with." They could hardly get together for a visit with a dead person!
I hope you have found this helpful.