Lightning Web Component実装例1

    public class listWrapper{
        @AuraEnabled
        public Boolean display{get;set;}
        @AuraEnabled
        public String texttext{get;set;}
        public listWrapper(
            Boolean display,
            String texttext
            ){
                this.display = display;
                this.texttext = texttext;
            }
    }

<template>
    <lightning-card title="Lnest Like" icon-name="utility:like">
        <div class="slds-grid slds-wrap slds-box">
            <div class="slds-form-element">
                <label class="slds-form-element__label" for="select-01">適当なラベル</label>
                <div class="slds-form-element">
                    <div class="slds-form-element__control slds-input-has-icon slds-input-has-icon_left">
                        <lightning-input type="search" placeholder="Filter" value={text_list} onchange={handleSBLFilterInput}></lightning-input>
                    </div>
                </div>
                <div class="slds-form-element__control">
                <select class="slds-select" id="select-01" multiple="" onclick={select_tettext}>
                    <template for:each={text_list} for:item="d">
                        <template if:true={d.display}> <!-- ←ここで出し分けしてる -->
                            <option key={d.key} value={d.texttext}>{!d.texttext}</option>
                        </template>
                    </template>
                </select>
            </div>
        </template>
    </lightning-card>
</template>

import { LightningElement, api, track,wire } from 'lwc';
import textlist_handler from '@salesforce/apex/yourClassName.textlist_handler';
import { NavigationMixin } from 'lightning/navigation'
import Id from '@salesforce/user/Id';

export default class Good extends NavigationMixin(LightningElement) {

    handleTextFilterInput(event){
        console.log("handleTextFilterInput");
        console.log(event.target.value);
        this.text_list.forEach((elem, index) => {
            const texttext_string = elem.lid.Native_language_Name__c + elem.lid.lnest_SBLvision__c + elem.lid.Alphabet_Name__c;
↑フィルター対象となる文字列。今回の実装の場合は、ラッパークラスにオブジェクトを含めてその中にある文字列を連結させています
            if(!texttext_string.toLowerCase().includes(event.target.value)){
                elem.display = false
            }else{
                elem.display = true
            }
        });
    }
}

                            <lightning-pill 
                                key={d.key} 
                                label={d.theme}
                                value={d.tl.LnestID_like_owner__c}
                                title={d.tl.Id}
                                onremove={sbl_theme_remove_handler}
                                name={d.myTLFlag}
                                >
                                <lightning-avatar src={d.iconurl} 
                                    fallback-icon-name="standard:user"
                                    alternative-text="User avatar"
                                    variant="circle">
                                </lightning-avatar>
                            </lightning-pill>