They were definitely synonyms and were interchangeable to a large degree. According to various dictionaries that Pleco references in its entry to「闕」:

• Pleco Chinese-English (PLC): Variant of 缺

• CC-CEDICT (CC): Used in place of 缺 (old)

• Cross-Straits (LAC): 脫漏。通「缺」。

• MOEDict (MOE): 脫漏的。闕字有二音，音ㄑㄩㄝ時義同「缺」。但使用習慣上仍見分別，如「拾遺補闕」、「疑闕」、「闕文」專詞多作「闕」，少用「缺」。

The last definition describes the modern usage differences between the two.

Note that to lack is unlikely to be the original meaning of either「闕」or「缺」:

• 闕, 門觀也。从門，欮聲。〔去月切〕(Basically,「闕」is a watchtower on a city wall; this is the Shuowen definition and AFAIK there's no evidence contradicting this.)
• 「缺」：從「缶」，「夬」聲。本義是器物破損。〔傾雪切〕

To lack could be interpreted as an extension of the original meaning of「缺」, and sometimes authors used「闕」for this meaning instead as a phonetic loan. Later on, the usage of「闕」and「缺」somewhat became differentiated.

They were definitely context-dependent variant representations of a single word and interchangeable to a large degree. According to various dictionaries that Pleco references in its entry to「闕」:

• Pleco Chinese-English (PLC): Variant of 缺

• CC-CEDICT (CC): Used in place of 缺 (old)

• Cross-Straits (LAC): 脫漏。通「缺」。

• MOEDict (MOE): 脫漏的。闕字有二音，音ㄑㄩㄝ時義同「缺」。但使用習慣上仍見分別，如「拾遺補闕」、「疑闕」、「闕文」專詞多作「闕」，少用「缺」。

The last definition describes the modern usage differences between the two.

Note that to lack is unlikely to be the original meaning of either「闕」or「缺」:

• 闕, 門觀也。从門，欮聲。〔去月切〕(Basically,「闕」is a watchtower on a city wall; this is the Shuowen definition and AFAIK there's no evidence contradicting this.)
• 「缺」：從「缶」，「夬」聲。本義是器物破損。〔傾雪切〕

To lack could be interpreted as an extension of the original meaning of「缺」, and sometimes authors used「闕」for this meaning instead as a phonetic loan. Later on, the usage of「闕」and「缺」somewhat became differentiated.