Given the context of the chapter, it appears the day of the Lord is after the tribulation, at the return of Christ when He gathers His elect, or shortly.
...because Paul says in 1Th5:1-3 that its ARRIVAL is "exactly like" the INITIAL "birth PANG [SINGULAR]" that COMES UPON a woman...
...and Jesus spoke of those very things ("the beginning of birth PANGS [PLURAL]") which will precede and LEAD UP TO His Second Coming to the earth
(...and THOSE are EQUIVALENT to the "SEALS" of Rev6... which are A PART OF what 1:1 / 1:19c / 4:1 is saying are "things which must come to pass IN QUICKNESS [NOUN]," i.e. IN the "7 yr" period that immediately precedes and LEADS UP TO His Second Coming to the earth / "RETURN" to the earth).
The VERY LENGTHY (earthly-located) time period known as "the day of the Lord" (which INCLUDES *all three* ASPECTS I just mentioned above) consists of: "a period of time of JUDGMENTs unfolding followed by a period of time of BLESSINGs unfolding" (<--ALL THAT="the DOTL" / and its related phrase "IN THAT DAY"!) Its "ARRIVAL" is the "FIRST SEAL" at the START of the "7 yr" period (not at its ENDING / Christ's "RETURN" to the earth Rev19).
[as I've mentioned in past posts, to go along with that ^ ] Wherever the phrases "the day of the Lord" and "IN THAT DAY" are used in close proximity / in same CONTEXTs, they are referring to THE SAME TIME PERIOD (and this is also the case in 2Th 1 & 2--BOTH CHPTS--where these two RELATED PHRASES are used, and refer to the SAME [future] TIME PERIOD)--Paul, in these two chpts, is contrasting the TWO DISTINCT "beliefs" ppl WILL BE coming to (FOLLOWING "our Rapture" event) when they are IN the Trib yrs...