If I understand correctly, the Find My network may be able to locate your iPhone if it's not connected to any cellular or WiFi network, but it won't be able to turn on Lost Mode. This is because Find My depend on the lost phone sending out pings which are picked up by other Apple devices nearby and then reported to Apple servers, but there should be no mechanism for these other Apple devices to tell the lost phone to go into Lost Mode.
If the lost phone has actually went into Lost Mode, then it means the phone actively checked in to Apple servers, and Apple told it to go into Lost Mode. It could be because someone turned Airplane Mode off via the Control Center, which does not require the phone to be unlocked, and the phone connected to cellular networks. However, since you said the phone is now in another country, your phone would have to have roaming data access for this to be possible. Is your lost SIM card still active, and does it have roaming data access?
Alternatively, it could be because someone restored the phone via DFU mode (this restores factory settings and wipes storage contents), and is attempting to activate it. During activation, the phone contacts Apple servers, which then ordered it to go into Lost Mode. If this is the case then your data is safe (because it has already been wiped), and whoever has possession of this phone cannot complete activation and use the phone, as long as you don't remove this phone from you Apple account. However, be on the lookout for phishing attempts on your Apple account credentials, because the possessor may want to steal your password in order to remove the activation lock.
In any case, do not remove the lost iPhone from your Apple account unless it returned into your hands.
