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Let's say someone has been sentenced to death and is about to be killed by lethal injection. While they are being brought into the execution room, they manage to escape the grip of the prison guards and try to escape. A short fight ensues during which a guard gets killed before the prisoner gets tazed and secured to the floor.

Was that killing legal? Is violence only considered self defense if it was used to protect oneself from illegal harm and not if that harm was mandated by justice? Do you have to accept death if you are sentenced to death or can you defend your life?

What if it later turns out, that you were wrongfully convicted or the execution would have been illegal due to some technicality: Can the killing of the prison guard be considered self defense now?

I assume this took place in Washington state. There are a number of self-defense provisions in Washington law. The first, RCW 9A.16.110, is primarily about reimbursements for prosecutions of acts of self-defense, but includes an applicable limit on prosecution:

No person in the state shall be placed in legal jeopardy of any kind
whatsoever for protecting by any reasonable means necessary, himself
or herself, his or her family, or his or her real or personal
property, or for coming to the aid of another who is in imminent
danger of or the victim of assault, robbery, kidnapping, arson,
burglary, rape, murder, or any other violent crime as defined in RCW
9.94A.030.

This provision is relevant, since executing a prisoner on death row is not a crime (the state Supreme Court recently struck down the death penalty, so I assume this took place before that ruling).

RCW 9A.16.020 states the more classic law on justified use of force, saying

The use, attempt, or offer to use force upon or toward the person of
another is not unlawful in the following cases:...(3) Whenever used by
a party about to be injured, or by another lawfully aiding him or her,
in preventing or attempting to prevent an offense against his or her
person, or a malicious trespass, or other malicious interference with
real or personal property lawfully in his or her possession, in case
the force is not more than is necessary;

Statutory law does not define offense against his or her person. Grabbing a person and strapping them down for some harmful purpose would normally constitute battery under the common law, but in this instance it is privileged, so it is not an offense against the person).

RCW 9A.16.030 says that

Homicide is excusable when committed by accident or misfortune in
doing any lawful act by lawful means, without criminal negligence, or
without any unlawful intent.

The person is under court order to be executed, and it is not lawful to resist that order. The guard, however, RCW 9A.16.040, may use deadly force pursuant to the legal mandate to carry out the court orde ((1)(b)"to overcome actual resistance to the execution of the legal process, mandate, or order of a court or officer, or in the discharge of a legal duty").

Do you have to accept death if you are sentenced to death or can you defend your life?

At this point the legal system has already decided you are going to die. I'm not quite sure what good it would do to worry about whether anything you do is legal. It's not like they can execute you twice.

In the 1998 case State v. Hobson, the Wisconson Supreme Court decided that it was illegal to resist an unlawful arrest. Footnote 19 sheds some light on what the law was like in other states at that time:

Eleven states have judicially abrogated the common law right to use physical force to resist an arrest which is unlawful but which does not utilize unreasonable force. See Miller v. State, 462 P.2d 421, 427 (Alaska 1969); State v. Hatton, 568 P.2d 1040, 1046 (Ariz. 1977); State v. Richardson, 511 P.2d 263, 268 (Idaho 1973); State v. Thomas, 262 N.W.2d 607, 610-11 (Iowa 1978); State v. Austin, 381 A.2d 652, 655 (Me. 1978); In re Welfare of Burns, 284 N.W.2d 359, 360 (Minn. 1979); State v. Nunes, 546 S.W.2d 759, 762 (Mo. Ct. App. 1977); State v. Koonce, 214 A.2d 428, 436 (N.J. Super. Ct. App. Div. 1965); State v. Doe, 583 P.2d 473, aff'd in part, rev'd in part, 583 P.2d 464, 467 (N.M. 1978); State v. Peters, 450 A.2d 332, 335 (Vt. 1982); State v. Valentine, 935 P.2d 1294, 1304 (Wash. 1997).

Seventeen other states have signaled their agreement by legislatively abrogating the common law defense. See Ala. Code § 13A-3-28 (1994); Ark. Code Ann. § 5-2-612 (Michie 1993); Cal. Penal Code § 834a (West 1985); Colo. Rev. Stat. § 18-8-103 (2) (1990); Conn. Gen. Stat. § 53a-23 (1985); Del. Code Ann. tit. 11 § 464(d) (1995); Fla. Stat. Ann. § 776.051(1) (West 1992); Ill. Ann. Stat. ch. 720, para. 5/7-7 (Smith-Hurd 1993); Mont. Code Ann. 45-3-108 (1995); Neb. Rev. Stat. § 28-1409(2) (1995); N.H. Rev. Stat. Ann. § 594:5 (1986); N.Y. Penal Law § 35.27 (McKinney 1987); Or. Rev. Stat. § 161.260 (1990); 18 Pa. Cons. Stat. Ann. § 505(b)(1)(i) (1983); R.I. Gen. Laws § 12-7-10 (1994); S.D. Codified Laws Ann. § 22-11-5 (1988); Tex. Penal Code Ann. § 9.31(b)(2), § 38.03 (West 1994)

The situation described is at least similar to resisting an unlawful arrest, even if it isn't identical. And some of the reasoning used is similar. The Wisconsin Supreme Court cited People v. Curtis, 450 P.2d 33, 36 (Cal. 1969):

In a day when police are armed with lethal and chemical weapons, and possess scientific communication and detection devices readily available for use, it has become highly unlikely that a suspect, using reasonable force, can escape from or effectively deter an arrest, whether lawful or unlawful. His accomplishment is generally limited to temporary evasion, merely rendering the officer's task more difficult or prolonged.

Similarly, in your scenario, the guards are going to execute the person whether or not he resists, and the only thing resisting will accomplish is to kill the guard before he himself is killed. It's likely not reasonable to expect that he would be able to escape the prison.