We don’t think we can know for certain.

Here’s the relevant passage from John (which is the only gospel that includes the spear/lance detail.

The Jews therefore, because it was the Preparation, and so that the bodies should not remain upon the cross on the Sabbath day (for that Sabbath day was a high day), besought Pilate that their legs might be broken and that they might be taken away. Then came the soldiers and broke the legs of the first and of the other who was crucified with Him. But when they came to Jesus and saw that He was dead already, they broke not His legs, but one of the soldiers with a spear pierced His side, and forthwith there came out blood and water. - John 19:31-34

So what kind of “spear” was it? Well, the author uses λόγχῃ / lonchē which is a pretty generic term for spear. What kind of soldier was it? The author uses στρατιωτῶν / stratiōtōn which is a generic term for soldier. So there’s no real contextual clue within the text itself. It could refer to just about any metal tipped wood shafted weapon spear, javelin, lance, etc.

If we take the gospel as, well, gospel, the soldiers who oversaw the execution were Pilate’s men, likely either from the legionary cohort that was stationed in the Fortress Antonia, or part of one of the Caesarea Maritima cohorts brought to Jerusalem to keep the peace during the holiday. So at the very least we can eliminate the possibility that these were part of Herod Antipas men or of the Sanhedrin’s guard. Unfortunately it’s not clear if such men would necessarily be regular legionaries or part of the Syrian auxilia which included both cavalry and archers. A pilum seems very likely, but something like a horseman’s lance can’t be eliminated.

I pulled the greek analysis from Strong’s Concordance, as my own Greek is far too rusty now a days.