To reproduce:
1. Open attached project;
2. Open "Compute" scene;
3. Make sure Lightweight Pipeline Asset is set in SRP Settings (Edit > Settings > Graphics > Scriptable Render Pipeline Settings);
4. Make sure Graphics API is set to Metal or Vulkan;
5. Enter Playmode;
6. Exit Playmode and remove LWRP asset from SRP Settings;
7. Enter Playmode again.

Expected result: Particles that use material with Compute shaders are drawn on the screen.
Actual result: Particles are not rendered on the screen with LWRP. With Built-in RP Compute shaders work as expected.

Reproduced with: 2018.1.9f2, 2018.2.10f1, 2018.3.0b4, 2019.1.0a3.

Notes:
-Reproduced with Android (Vulkan), iOS (Metal), MacOS (Metal)
-No errors are thrown
-You can see particles in the Scene window