No, Lawrence did not increase the amount, but in 1940 Segre got a contract directly from University of California that brought his monthly salary back to $300. Below are details.
From Segre's memoirs "A Mind Always in Motion: the Autobiography of Emilio Segrè." Berkeley, California: University of California Press, 1993.
In 1939, \$300 a month was a good salary, and it got me out of the woods for some time, but after six months, in July 1939, Lawrence, who by then must have realized my situation, asked me if I could return to Palermo. I answered by telling him the truth, and he immediately interjected: "But then why should I pay you \$300 per month? From now on I will give you \$116." I was stunned, and even now, so many years afterward, I marvel at Lawrence's impulsiveness; he did not think for a second of the impression he conveyed. With a minimum of reflection and diplomacy, he could have saved his \$184 a month without cutting a horrible figure in my eyes. However, although I have not forgotten his conduct, I now see it in a different light than I did then. I did not know what the salaries of other members of the Rad Lab were at the time. It was I who, with \$300 a month, was the exception, and salaries around \$116 were not rare. If I had known this and how Lawrence behaved with Americans who were unemployed because of the depression, I might have viewed the episode somewhat differently. I was somewhat older and better established as a scientist than some excellent Americans were, but they too got meager salaries, although they had academic positions and guaranteed careers. In any case, with a wife and a child, a salary of \$116 was scant, but it was not totally impossible to live on it. With \$200 a month I could make ends meet, sparingly, but without deprivation, and I could bring my salary to that level by using my private funds, the existence of which was known only to Elfriede and to my friend Emo, whose discretion was absolute.
In the summer of 1940, we were visited at Berkeley by the head of the physics department at Purdue University, Karl Lark-Horovitz. He was of Austrian origin, of a touchy and sullen character that made him many enemies, but at heart a very decent man and a good physicist. At Purdue he had created an excellent physics department and ruled it autocratically, but with good results. He recognized quality in science and helped whoever he thought merited it. When I became acquainted with him, I felt I could openly tell him my personal problems. He invited me to go to Purdue for a limited period. He could not secure a permanent job for me, but thought that even a temporary appointment would greatly improve my position at Berkeley. Thus in the fall of 1940, Elfriede, Claudio, and I took the train for West Lafayette, Indiana. At Purdue, we settled in at Union Hall, which was strongly heated and
extremely dry, so much that in walking on its insulating carpets, one got highly electrified, and I could amuse Claudio by pulling sparks from his nose. I had also prepared some experiments I could easily and rapidly carry out, and I did my best to elicit appreciation for my lectures. Lark Horovitz's plan worked to a fault. Things went well, and I was pleased.
At Berkeley, when they perceived that I was really leaving, Lawrence and the head of the physics department, Raymond T. Birge, found the money to pay me and wired me with the offer of a lecturership. It was not a tenured position, but it was great progress. I had, more or less, returned to the position with which I had started in 1938, before they knew I could not return to Italy. I asked for a contract with the University of California, not with the Rad Lab, of which I had had enough. I knew that Birge kept his word, whereas Lawrence's intentions and capabilities could change at any time. In any case I would have access to the cyclotron, and I hoped that relations with Lawrence would improve, because having good work done by me in the Rad Lab at no expense to himself, he would be happy and sweet, as indeed happened. Thanks to Lark-Horovitz, I had \$300 a month and a much improved position.