Is there a way to make Lackey output a specific set of dialogue when a card is placed onto the field in a specific way, if it meets a specific condition?
In Vanguard (and other games, notably Weiss Schwarz), the main mechanic is "Drive", where you turn over the top card of your deck and see if it's a Trigger (of which there are four kinds). As it stands, it's possible to make a Trigger button which will place the top card of the deck into play and read off what it is, but I'd really like to know if there's a way to make it reference the card's Trigger type (which is obviously recorded in the setfiles) and also declare that.
No, that is not currently possible, but I don't think it would be particularly helpful to do that. The log will show that you are using the Drive mechanic (playing it from the deck). And what you are asking (i think) is for the log to say some additional thing, but instead of looking at the log, people can just look at the card, which I think they would prefer to do anyway.
Most people don't, since it adds an extra step, but oh well.