[SalesForce] convert text field to lookup field in salesforce

It is a known limitation of Salesforce1 Mobile and is documented in the Salesforce1 App Developer's Guide.

From the Salesforce1 App Developer's Guide section, Visualforce Components to Avoid in Salesforce1:

Using <apex:inputField> is fine for fields that display as a basic input field, like text, email, and phone numbers, but avoid using it for field types that use an input widget, such as date and lookup fields.

And, from the Unsupported Visualforce Components section:

<apex:inputField> for field types that use a widget for input, instead of a basic form field

Additionally, a web developer from Salesforce.com answered the question you referenced (Lookup fields using Salesforce1 and Visualforce) with an answer that stated they weren't supported in that way, so it's a safe bet that's the case. ;)

I did not see any Ideas, either, when I searched for 'Salesforce1': https://success.salesforce.com/ideaSearch?keywords=salesforce1.

I'm not aware of a quick/easy way. Depending on your situation you could try an autocomplete, e.g., jQuery Mobile - Remote autocomplete.

Lookup fields such as your Object1__c.Object2__c field can have a lookup filter defined. To exclude the already selected Object2__c instances in such a filter, you then need say a checkbox field Object2__c.InUse__c to use in the filter expression. A trigger can populate that checkbox field on insert/update/delete/undelete of Object1__c.

The trigger would look like this in its basic form:

trigger Object2InUse on Object1__c (after insert, after update, after delete, after undelete) {
    Set<Id> o2Ids = new Set<Id>();
    if (Trigger.isInsert || Trigger.isUpdate || Trigger.isUndelete) {
        for(Object1__c o1 : Trigger.new){
            if (o1.Object2__c != null) o2Ids.add(o1.Object2__c);
        }
    }
    if (Trigger.isUpdate || Trigger.isDelete) {
        for(Object1__c o1 : Trigger.old){
            if (o1.Object2__c != null) o2Ids.add(o1.Object2__c);
        }
    }
    if (o2ids.size() > 0) {
        Map<Id, Integer> m = new Map<Id, Integer>();
        for (Id id : o2ids) m.put(id, 0);
        for (AggregateResult ar : [
                select Object2__c i, count(id) c
                from Object1__c
                where Object2__c in :o2ids
                group by Object2__c
                ]) {
            m.put((Id) ar.get('i'), (Integer) ar.get('c'));
        }
        Object2__c[] o2s = new Object2__c[] {};
        for (Id id : m.keySet()) {
            o2s.add(new Object2__c(Id = id, InUse__c = m.get(id) > 0));
        }
        update o2s;
    }
}

and the filter criteria on the Object1__c.Object2__c field would be:

Object 2: In Use EQUALS False