You can solve this problem like this

In App.Svelte

<script>
  import Checkbox from './Checkbox.svelte';
    
  let schema = {
    name: "bar",
    vars: [{ name: "X" }],
  };

  $: availableLTs = ["aaa", "bbb", "ccc", "ABC"];   
  $: matchesSearch = availableLTs.filter((elem) =>{ return elem.includes(searchString); })

  let selectedChart = 'bar'; 
  let selectedVars = {X: { lts: [] }};
  $: console.log(selectedVars)
  $: schemaVars = schema.vars;
  let searchString = "";
</script>

<main>
  {#each schemaVars as {name}}
    <h6>
      {name}
      <input type="text" bind:value={searchString} placeholder="Search..." />
    </h6>
    <Checkbox bind:value={selectedVars} {name} {matchesSearch}/>
  {/each}
</main>

In Checkbox.Svelte

<script>
    export let value, name, matchesSearch;
</script>

{#each matchesSearch as ele}
    <div class="form-check">
        <label>
            <input
                         type="checkbox"
                         class="form-check-input"
                         bind:group={value[name].lts}
                         value={ele}
            /> 
            {ele}
        </label>
    </div>
{/each}

You can check it in this repl

Looks like the problem has something to do with the nested each loops

  {#each schemaVars as schemaVar}
    ...
    {#each availableLTs as ele}
      
    ...//Checkbox

    {/each}
  {/each}

which can be solved through wrapping the inner loop inside a component.

The previous answer almost solved the problem, but one important thing is missing: The each loop inside the component is not a "keyed each block" ->

1. select the third checkbox 'ccc'
2. filter for 'c'
3. -> 'ccc' moves to the first position and is not checked anymore

(alternatively select 'aaa' and filter for 'b'...)

This can be solved by adding the label text as key/id (assuming that the checkbox labels are unique) ->

{#each filteredLTs as ele (ele)}        
        ...
{/each}

Since the problem wasn't the way the variable was set (...selectedVars[schemaVar.name].lts}), I would try to keep the logic inside the component general and set the variables specifially inside the component tag inside App.svelte -> the component stays universal and can be easyly reused Example in this REPL

[App.svelte]

<script>
import Checkboxes from './Checkboxes.svelte'
    
let schema = {
   name: "bar",
   vars: [{ name: "X" }],
};

let allLTs = ["aaa", "bbb", "ccc", "abc"];
let searchString = "";
    
$: filteredLTs = allLTs.filter(lt => lt.includes(searchString)) 
let selectedVars = {X: { lts: [] }};
    
$: console.log(selectedVars.X.lts)
    
</script>

<main>
  {#each schema.vars as schemaVar}
    <h6>
      {schemaVar.name}
      <input type="text" bind:value={searchString} placeholder="Search..." />
    </h6>
    
    <div class="form-check">
    <Checkboxes checkboxes={filteredLTs} bind:checked={selectedVars[schemaVar.name].lts}/>
  </div>
  {/each}
</main>

[Checkboxes.svelte]

<script>
    export let checkboxes, checked  
</script>

{#each checkboxes as checkbox (checkbox)}        
        <label>
            <input
              type="checkbox"
              class="form-check-input"
              bind:group={checked}
              value={checkbox}
            />
            {checkbox}
   </label>
{/each}