Yes, some observers drew parallels between the two events. In fact, Pakistan itself was aware of this, as was India. In a Christian Science Monitor article from May 21, 1948, the article says:

Although it is a country which owes its existence to a partition, Pakistan opposes partition of Palestine on the ground that it is not analogous to the partition of India.

It goes on to list Pakistan's reasons. But it's clear, at least from that, that observers were aware of potential parallels. Another example is a New York Times article from October 8, 1947, where Pakistan also said it did not see the situations as analogous. The article says:

The Pakistani [delegate to the United Nations] noted that his own nation had been formed by partition, but he said Palestine was not analogous.

Others were aware of it too in other fora. It's unclear to me, however, that anyone used "lessons" learned for the partition of the Palestine Mandate. I can't find many links to it, at any rate. Sorry I don't have a more comprehensive answer; I genuinely couldn't find enough beyond more examples of people acknowledging the analogy and seeking to differentiate, usually done by Pakistan.