Given that we know of the war crimes committed by Israel such as forcible expulsions such as Lydda or massacres like Deir Yassin, I was wondering to what extent the holocaust survivors fighting for Israel were complacent or involved.

This is a bit of a loaded question.

For one, "Israel" as an entity did not exist at the time of Deir Yassin (April 9, 1948). It was still a formed, but also forming entity at the time of Lydda (July 1948). So what constituted "Israel" is rather unclear, when all's said and done.

Furthermore, what actually happened is also unclear in both instances. In Deir Yassin, there's no dispute that there was a massacre at this point, but more recent evidence suggests the number of dead were inflated by as much as 2-3x by both Irgun and the Arab armies, and that half of the dead were not civilians at all. The Irgun forces were relatively small, never having more than 5,000 or so total, and the Deir Yassin massacre was perpetrated by a small contingent of roughly 120 Irgun members, meaning it is unlikely that a large number were Holocaust survivors. By the end of 1948, according to Yablonka, roughly 88,000 people were in the IDF, the vast majority being former Haganah, and not Irgun. It was during the period from June to December of 1948 that most Holocaust survivors are believed to have joined the IDF, totaling 22,000 total. But they were under the command of Haganah leaders, as Irgun had been forcibly disbanded in June 1948 and dispersed.

Thus, it is likely that their involvement in the actions at Deir Yassin were minimal at best. Potential involvement there by the Palmach also doesn't seem to have been likely to include Holocaust survivors in any large numbers.

Moving to Lydda, there's the possibility for more involvement. But while there was that possibility, there was also the possibility that Lydda was not a massacre at all, as argued by historian Martin Kramer. Historically speaking, there's reason to believe the claim of an expulsion order having been given by Ben-Gurion was also misreported by Rabin. At any rate, when word reached the Israeli Cabinet of the planned expulsions, they issued an order stating that anyone who wished to go could, but anyone who stayed would be responsible for their own supplies. And regardless of the orders and any delays between them, historians believe the residents of Lydda now wanted to leave, being fearful of further fighting and of the stories they'd heard of events like Deir Yassin, both propagated by Irgun members in the past and also by Arab armies. So while some were expelled, some fled, and some who were expelled also wanted to leave regardless.

As for Holocaust survivor involvement here, it's also difficult to say. There is, again, the evidence that this was only towards the start of most Holocaust survivors joining the IDF. I've not seen any accounts of Holocaust survivors who were involved, though I have heard that some exist anecdotally through people I know. I may have to get back to you on that. It's unclear though if they would have felt guilt, given that Israel's leaders and many of those involved in the fighting viewed the alternative to victory (and many of the actions they took) as a path to genocide, based on the rhetoric of Arab leaders and commanders at the time.