Another important description of the intermediate state between death and resurrection can be found in Josephus: "People depart from this life in accordance with nature's law, thus repaying what God had lent them .... Their souls (hai psukhai) remain without blemish, and obedient, and receive the most holy place in heaven. From there, when the ages come round again, they will again be sent into holy bodies" (Jewish War, 3.8.5). Revelation also makes reference to the "souls" (psukhas) of the righteous martyrs waiting in heaven for their vindication and future resurrection (cf. 6:9-11, 20:4). This language is influenced by Platonism, which uses the word "soul" to refer to the essence of the person that leaves the body at death; in older Semitic anthropology the word refers to the embodied person. In the Testament of Abraham, we have an account of the spirit of Abraham being taken into heaven while his body is buried on the earth, and this story has an interesting connection with Luke because it refers to the other patriarchs as residing in Abraham's "bosom" in heaven (compare Luke 16:22-31). In the Assumption of Moses known to the church fathers, there was a story about Joshua seeing Moses "double" after he died, one Moses being taken into heaven while the other Moses was the corpse awaiting burial (Jude 9 apparently alludes to the conclusion of this story).
The view of Jesus' resurrection in Luke seems to along these lines, that at death Jesus in the spirit was taken into Paradise (like Lazarus) while in the body he was buried into the earth for parts of three days. Thus, Jesus commits his spirit into the hands of the Father at his death (Luke 23:47), while his soul (in the older Semitic sense, through allusion to the OT) lies in Hades where it could experience "corruption" (through corruption of the body) but which was raised back to life (Acts 2:23-33). The logic of the argument in Acts 2 is that David was not referring to himself when he wrote Psalm 16 for his tomb (and hence his body) was "still with us", so he must have been referring to Jesus who was raised as a whole person back to life and taken up into heaven (Luke 24:51, Acts 1:9). This does not preclude for Jesus an intermediate state which generally precedes resurrection, but there were different ideas on where the righteous reside during their intermediate state, whether in God's abode in heaven (= Paradise) which is the case in Revelation, Testament of Abraham, Josephus, and other sources, or in certain chambers of Sheol/Hades as is the case in 1 Enoch, 4 Ezra, and other texts. The tradition that Jesus spent his intermediate state in the spirit in Hades is not found in Luke-Acts but in other sources that develop the proto-gnostic descent myth (found in Ignatius, the Epistula Apostolorum, and later more mature gnostic texts) into a descensus ad infero myth (found in Odes of Solomon, Ascension of Isaiah, and other texts; 1 Peter 3:18-20 may form part of this tradition, but it is problematic in its interpretation).
Paul actually has some very close parallels with Luke 23:43. In 2 Corinthians 5:1-10, he states that when "we are at home in the body we are away from the Lord" (v. 6), while in death we are "away from the body and at home with the Lord (pros ton kuriou)" (v. 8). This wording suggests that immediately at death (= "today") one goes to heaven to be with Jesus, an idea that appears in Luke 23:43. Similarly, in Philippians 1:23-24, Paul muses over whether he should "remain in the body" (= stay living in the flesh) or "depart (= die) and be with Christ (sun Khristó einai)". Finally, when discussing the advent of the Lord and the raising of the faithful to heaven, Paul states that then "we will be with the Lord (sun kuriou esometha) forever" (1 Thessalonians 4:17). The author of Luke seems to be retrojecting the post-resurrection situation between dying believers and Christ into the intermediate state prior to Jesus' resurrection.