Their penalty shoot-out victory at Stourport in the previous round was their fifth in the competition so far this season, and with it came the reward of the visit of the Eastern Counties League Premier side - as well as the chance to take another step towards emulating the achievements of the Valley 1983 team that famously triumphed at Wembley to lift the Vase trophy.
Town Director Neil Melvin looked forward to the clash: "We've had a few significant encounters at the club since the turn of the century in the FA Cup qualifying phase and the FA Trophy (in 2003) and also in end of season play-off fixtures, but the opportunity to reach the last 16 of a national competition must be up there with - or arguably beyond - them."
Saturday's opponents Lakenheath will be making their first ever appearance at this stage of the Vase following their last gasp win over Shefford Town & Campton in the Third Round, having been promoted to the same level of the non-league pyramid as Rugby in the summer - also for the first time in their history.
The Suffolk club currently sit in 11th spot in their division with seven wins, seven draws and eight defeats to their name, but Valley boss Carl Adams knows it will be a tough test at the weekend.
He said: "It's great that we have got a home draw and we have to try and make that advantage count, but there are no easy games at this stage of the competition."
If they are to make Monday's Fifth Round draw, Town will have to quickly bounce back from their disappointing display at home to Hinckley LR last Saturday, when their ten match winning run came to an end in the 3-0 defeat against the UCL Premier league leaders at Butlin Road.
Rugby pretty much failed to land a glove on a side that continued their excellent form in the league this season thanks to first half strikes from Callum Earls and Matt Langham, and then a further goal from skipper Danny Jenno in the second to seal the three points.
Town's best opportunity on the day came when David Kolodynski 's header drew a fine save from Will Highland just before the interval, but they were generally outplayed by a Hinckley side that extended their lead at the top of the table with a record of 20 wins and a draw from their 21 games played.
The defeat saw Valley slip a place to 4th in the rankings following Newport Pagnell's victory at another of the top teams Coventry United.
Adams is sweating on the fitness of a number of key players ahead of Saturday's clash though, with both Jamal Clarke and James Hancocks joining Luke English on the sidelines for the Hinckley game.
English's fractured foot is likely to rule him out for a couple of further weeks, but there is a chance the other two may return for the Vase, although Adams will definitely be without the cup-tied trio of Adam Shaw, Alex Lock and Madundo Semahimbo.