Luring a child is a felony in Canada: see Canada Criminal code 172.1:
172.1 (1) Every person commits an offence who, by a means of telecommunication, communicates with
(a) a person who is, or who the accused believes is, under the age of
18 years, for the purpose of facilitating the commission of an offence
with respect to that person under subsection 153(1), section 155,
163.1, 170, 171 or 279.011 or subsection 279.02(2), 279.03(2), 286.1(2), 286.2(2) or 286.3(2);
and further paragraphs specify different ages and offenses. Cutting through the section number jungle, this covers any attempt to have sex with a minor. This law does not punish having sex with a minor (that's separate), this covers communication with that end in mind. The fact that the would-be child is an adult is irrelevant:
(3) Evidence that the person referred to in paragraph (1)(a), (b) or
(c) was represented to the accused as being under the age of eighteen
years, sixteen years or fourteen years, as the case may be, is, in the
absence of evidence to the contrary, proof that the accused believed
that the person was under that age.
If a 21 year old represents himself as being under 18, that fact proves that the accused has the requisite belief.
The Canada Dept. of Justice has a position on citizen's arrests, which would suggest "no you can't" (rather, you should call the police). That however is a suggestion, not a legal requirement. It is, however, correct, according to the law itself (federal), Criminal Code s. 494, which states:
(1) Any one may arrest without warrant
(a) a person whom he finds committing an indictable offence; or
(b) a person who, on reasonable grounds, he believes
(i) has committed a criminal offence, and
(ii) is escaping from and freshly pursued by persons who have lawful authority >to arrest that person.
The first condition sanctioning warrantless arrest is finding a person committing an indictable offense. The problem here is that in these scenarios, the arresting person has a reasonable suspicion that the accused has commited such an offense, but they did not find them committing such offense. Under (b), a reasonable belief arrest includes not only "has committed" but also "is escaping from and freshly pursued by persons who have lawful authority to arrest that person", and the latter is not the case.
Since this would not be a lawful arrest, it would be unlawful battery (and other things, perhaps). Provincial law is unlikely to widen the scope of a citizen's arrest,