Based on Picklist Visible Lookup Field

Here "Risk Assessment" is a Picklist and "Peer Reviewer" is a Lookup field.

<apex:pageBlockSectionItem >
 <apex:outputLabel value="Risk Assessment"></apex:outputLabel>
  <apex:actionRegion>
   <apex:inputField value="{!thisCon.theCase.Risk_Assessment__c}" rendered="{!thisCon.caseRTN       ame == 'OD Change'}"> 
    <apex:actionSupport event="onchange" rerender="pr,prr" />      

  </apex:inputField>
 </apex:actionRegion>
</apex:pageBlockSectionItem>
  
<apex:pageBlockSectionItem >
 <apex:outputLabel value="Peer Reviewer"></apex:outputLabel>
  <apex:outputPanel id="pr"> 
   <apex:outputPanel rendered="{!if(thisCon.theCase.Risk_Assessment__c != null,true,false)}"> 
   <apex:inputField value="{!thisCon.theCase.Peer_Reviewer__c}" rendered="{!thisCon.caseRTNam        e == 'OD Change'}" required="true"/>
  </apex:outputPanel>
 </apex:outputPanel> 
</apex:pageBlockSectionItem>

This is another way:-

 <apex:actionRegion >
  <apex:inputField value="{!thisCon.theCase.Risk_Assessment__c}" required="true" rendered="{!     thisCon.caseRTName == 'OD Change'}">  
   <apex:actionSupport event="onchange" rerender="pr,rp" />      
  </apex:inputField>   
 </apex:actionRegion>
   
 <apex:pageBlockSectionItem >
  <apex:outputPanel id="rp" >
   <apex:outputText value="Risk Assessment" rendered="{!if(thisCon.theCase.Risk_Assessment__c       != null,true,false)}"/>
  </apex:outputPanel> 

 <apex:outputPanel id="pr">
  <apex:outputPanel rendered="{!if(thisCon.theCase.Risk_Assessment__c != null,true,false)}">
   <apex:inputField value="{!thisCon.theCase.Peer_Reviewer__c}" rendered="{!thisCon.caseRTNam         e == 'OD Change'}" />
  </apex:outputPanel>
 </apex:outputPanel>  
</apex:pageBlockSectionItem>