To the east of the circular font, there is a badly damaged rectangular basin, which measures about 2,2 x 1,35 m. On the south short side, there is a kind of nich with the bottom 15 cms above the bottom of the rectangular basin. What was its original shape? Perhaps one can compare with some earlier Roman nymphaea from Pompeji with a kind of aedicula with a nich in front of a low basin, and reconstruct the two basins as in this drawing.  
  
Washing of feet after baptism 

The secondary, rectangular basin may have been used for the washing of feet, imitating what Jesus did to the Apostles in John 13. On this page, some of the evidence for this rite will be discussed. 

Some sources mention this rite as a part of baptism after immersion and anointing. St. Ambrose in Milan wrote in 380-390 that this part of the rite had been left out in Rome. For this reason, the secondary basin in San Lorenzo in Lucina could be used for the washing of feet only if the baptistery was built some time before Ambrose wrote, in the mid fourth century.  
 
 

Ambrose writes:  "The Church of Rome does not have this custom, whose character and form we follow in all things. Yet it does not have the custom of washing the feet. perhaps on account of the multitude this practice declined."  (De sacramentis 3,5: Sources chrétiennes 25bis)  (The full Latin text can be read here)

 
The fourth century was a period when the washing of the feet was left out not only in Rome but also in Spain. Already in 305, the council of Elvira states in its canon 48 that the rite should be abrogated. 
 

The council of Elvira states:  Emendari placuit, ut hii qui baptidiantur, ut fieri solebat, nummos in conca non mittant, ne sacerdos quod gratis accepti pretio distrare videatur. Neque pedes eorum lavandi sunt a sacerdotibus vel clericis.  (Text in: Jose Vives, Concilios Visigoticos e Hispano-Romanos, Madrid 1963, 10)

As the fourth century seems to be the period when this rite was suppressed, the interpretation of the secondary basin in the baptistery of San Lorenzo in Lucina depends to a great extent upon the date of the church and its baptistery. 
 

Usually, the church and the baptistery have been dated to 432-440 through the identification with a church built to honor the Roman martyr Laurentius (Lawrence). The washing of feet was never reintroduced in Rome, so a 5th c basin for feet washing in Rome would be impossible. 

However, we may have to consider the possibility that the church and the baptistery may be older, from the middle of the 4th c. 

The main difficulty of this interpretation of the secondary basin is chronological: most scholars have dated the basilica, and thus the baptistery, to the fifth and not the fourth century. 

The advantage is that this interpretation could explain why similar secondary basins generally are not found in other  baptisteries in the Roman parishes (tituli), which usually are dated after the fourth century. Any other interpretation of the basin must also explain why similar basins are not found elsewhere in Rome. 
 
 

Read more about the washing of the feet as Christian initiation in:   M. Pesce - A. Destro, "La lavanda dei piedi di Gv 13,1-20, il Romanzo di Esopo e i Saturnalia di Macrobio", Biblica 80, 1999, 240-249.   J. Sammer, "Why Did Jesus Wash His Disciples Feet?", Aeon. A  Journal of Myth and Science III, 4, 1993, 21-23.  Victor Saxer, Les rites de l'initiation chrétienne du IIe au VIe siècle   (Centro italiano di studi sull'alto medioevo 7), Spoleto 1988.