Steam Client could Lag or crash due to many reasons like it could be the game you downloaded or it could be the bug in the software itself. Whatever it may be here are some methods to solve this lag or crash problem.
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Clear your steam browser cache and cookies
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Clear your download cache
I cannot explain the each step but you can look this up if you want step by step guide. My problem was solved when I cleared my browser cache and cookies though so try that method first.