In what stage of bacterial growth can penicillin inhibit the growth of the cellular wall?
This is a really good question that requires you to appreciate a few different details and to overcome a few implicit assumptions that you might perhaps have.

The bacterial growth stages you refer to only apply to a population of bacteria. Individual cells do not undergo these stages.
Relatedly, bacterial population growth stages are independent of the stage of bacterial cell wall growth.

You can have mature or immature bacteria at any stage of &quot;bacterial growth&quot;, with either fully formed walls, or with none. This understanding should answer your question partially.
Here are a few more things to consider, for a more complete understanding:

Penicillins are a class of molecules, of varying efficacy and bioavailability across the body and across different kinds of walls and membranes.
Inhibiting the spread of bacteria can be achieved using two types of antibiotics... bactericidal or bacteriostatic ones. Bactericidal means the bacteria die, while bacteriostatic means their growth is slowed or stopped.
Penicillins are bactericidal agents that exert their mechanism of action by inhibition of bacterial cell wall synthesis and by inducing a bacterial autolytic effect. So even mature bacteria will die off in the later stages of outgrowth. In principle, it does not matter what growth stage the bacteria are at, the bactericidal mechanism will take place regardless.
Pencillins are more effective against Gram-positive bacteria. Gram-negative bacteria have a lipopolysaccharide and protein layer that surrounds the peptidoglygan layer of the cell wall, which acts as a barrier for the penicillin from reach its target (which is responsible for completing the synthesis of peptidoglycans, the structural component of bacterial cell wall). However, penicillin can get into Gram-negative cells, for example through channels called porins.

This is more or less very standard knowledge that is easy to look up. Wikipedia's entry on penicillin is a good place to orient yourself if you already haven't.