Lemon juice and carbonic acid reaction
These two weak acids have similar disassociation constants in water.  A low Ka indicates a relatively small number of acid molecules will form an anion stabilized by water.  Two weak acids with similar disassociation constants will coexist in a solution without interacting.  If two weak acids have very different Ka then there can be a reaction.  In this case nothing would happen.   For more generalized information search for mixture of weak acids.


  Carbonic Acid


$$\ce{H2CO3 + H2O &lt;=&gt; HCO3- + H3O+}$$
$$K_a = 4.3 \times 10^{-7} = \frac{[\ce{H3O+}][\ce{HCO3^-}]}{[\ce{H2CO3}]}$$


  Citric Acid


$$\ce{H3C6H5O7 + H2O &lt;=&gt; H2C6H5O7- + H3O+}$$
$$K_a = 1.8 \times 10^{-6}  = \frac{[\ce{H3O+}][\ce{H2C6H5O7^-}]}{[\ce{H3C6H5O7}]}$$