How is the protease inhibited by lopinavir different in SARS-CoV-2 compared to SARS-CoV?
Is there a difference in the gene encoding for the protease?

This paper by Wu et al. annotates the SARS-CoV-2 genome and compares its divergence from other coronaviruses, which may help answer your second question.

This annotation includes 16 genes for non-structural protein ("nsp"). Supplemental materials for this paper indicate that all but two of these proteins (nsp7 and nsp13) have amino acid substitutions between SARS-CoV-2 ("2019-nCoV" in the paper) and SARS-CoV. 

The gene nsp5 encodes 3CLpro (chymotrypsin-like cysteine protease), so there are differences there. 

Literature suggests nsp5 and other non-structural proteins are potential targets for a number of antiviral therapies.

Another paper suggests further that lopinavir targets nsp3 products, among other proteins, in use against SARS-CoV:


  Lopinavir’s possible target is Nsp3b, Nsp3c, helicase, NRBD or E-channel with the mfScores of –158.050, –189.140, –114.018, –171.127, and –221.785, respectively.


The nsp3 gene contains a papain-like protease 2 (PL2pro) domain. Supplemental materials from the first linked paper suggest nsp3 has a different amino acid sequence between SARS-CoV and SARS-CoV-2. 

It might be worth digging into the Wu et al. paper and the raw annotation data to look at what those a.a. substitutions are, to see if that might help in determining why lopinavir is not as efficient at inactivating PL2pro and reducing levels of the novel coronavirus.

It may also be worth considering the target itself. Going back to the Nature Biotechnology article:


  But Erik De Clercq, of the Rega Institute for Medical Research in Leuven, Belgium, says that in searching for or designing effective drugs against COVID-19: “We should stay away from antivirals known to be acting at targets not playing a role in the replication of coronaviruses.” Such drugs include penciclovir, which is targeted at the herpesvirus DNA polymerase, and lopinavir/ritonavir, which are targeted at the HIV protease. Instead, he would favor targeting a virus-specific protein such as the RNA-dependent RNA polymerase, noting that coronaviruses do not contain or use a reverse transcriptase.