Here is the Obama justification for killing Anwar al- Awlaki, an American terrorist in Yemen. The Obama administration posited the following legal theory:
...By its nature, therefore, the threat posed by al-Qa’ida and its associated forces
demands a broader concept of imminence in judging when a person continu-
ally planning terror attacks presents an imminent threat, making the use of
force appropriate. In this context, imminence must incorporate considerations
of the relevant window of opportunity, the possibility of reducing collateral
damage to civilians, and the likelihood of heading off future disastrous attacks...
This quote is from https://bit.ly/30joIQL, a link to a paper arguing generally for necessity subsuming imminence as the one criterion for for justified self defense. The paper deals principally with domestic instances but in Part V, starting at page 22, it accessibly and straight forwardly deals with imminence as an essential element in justifiable self defense in international relations.
The thrust of the argument, btw, in Part V is that the language of imminence in such situations is linguistic window dressing to attempt to meet conventional legal formulae for the legal use of force. In reality, the argument is, necessity supplants imminence and imminence is a distraction in these kinds of contexts.
That the previous administration made this argument doesn’t necessarily make it legitimate but it ought at least give pause to reflexive arguments from partisanship that what Trump did here was obviously illegal—ie, the shoe on the other foot test.