"Either I create that column with the time value, or i can fool vlookup by doing the request including the same date that is in the time value in the table."
Unless you create the "column with the time value," there is no "time value in the table". That is true for both tables.
EVERY cell that displays a Time (of day), EVERY cell that displays a Date, and EVERY cell that displays a date and a time (of day) contains a Date and Time Value. Period. Full Stop. The date part (or the time part) could be hidden, but it is still there.
The column labeled "Tval" and the one labeled "Time value" contain numbers. The number is produced by the TIMEVALUE(date-and-time) function. TIMEVALUE() ignores the date part of a Date and Time Value, and returns the fraction of a 24 hour day represented by the time part of that Date and Time Value.
If you use the numerical values produced by TIMEVALUE as the search-for value in VLOOKUP, and the column containing the numerical values produced by TIMEVALUE as the first column of the search-where value in VLOOKUP, the formulas will work as displayed above, and will not be affected by any difference in the date part of the D&T values in column A of the two tables.
If you instead use the D&T values in column A for search-for and search-where, you need to include a date in your search term, ot to "fool" VLOOKUP, but to give it a value that exactly or closely matches one of the values on the lookup table. If you simply enter the time of day as the search value, VLOOKUP will always return the closest match to the Date and Time value resulting from that entry. On any day later than the date the lookup table was created, the close match will be the last item on the table (ie. the Date and Time that is most recent)
Regards,
Barry