How can we apply two vlookups together on a single cell?

if I get your question correctly 

you can use:

1. concatenate
2. logical operators functions OR(),  AND() ...

sd

I used below formula in a single cell to get the results in E1, if you consider "sd" is in Cell A1 and accordingly.

=VLOOKUP(D1,A:B,2,0)&VLOOKUP(D:D,A:C,3,0)